Showing papers in "International Journal of Mathematics and Mathematical Sciences in 2020"
TL;DR: A generalized SEIR model of COVID-19 is proposed to study the behaviour of its transmission under different control strategies and the impact of various intervention strategies, including voluntary quarantine, isolation of infected individuals, improving an individual’s immunity, and hospitalisation are pretended.
Abstract: On 11 March 2020, the World Health Organization declared the outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2) a pandemic and a Public Health Emergency of International Concern. As of 29 March 2020, coronavirus disease 2019 (COVID-19) has affected 199 countries and territories, resulting in 683,536 positive cases and causing 32,139 deaths. The pandemic has the potential to become extremely destructive globally if not treated seriously. In this study, we propose a generalized SEIR model of COVID-19 to study the behaviour of its transmission under different control strategies. In the model, all possible cases of human-to-human transmission are considered and its reproduction number is formulated to analyse the accurate transmission dynamics of the coronavirus outbreak. Optimal control theory is applied to the model to demonstrate the impact of various intervention strategies, including voluntary quarantine, isolation of infected individuals, improving an individual's immunity, and hospitalization. In addition, the effect of control strategies on the model is analysed graphically by simulating the model numerically.
26 citations
TL;DR: A mathematical model for Lassa fever disease transmission under the assumption of a homogeneously mixed population is formulated and the optimal control theory is invoked so as to determine how to reduce the spread of the disease with minimum cost.
Abstract: Lassa fever is an animal-borne acute viral illness caused by the Lassa virus. This disease is endemic in parts of West Africa including Benin, Ghana, Guinea, Liberia, Mali, Sierra Leone, and Nigeria. We formulate a mathematical model for Lassa fever disease transmission under the assumption of a homogeneously mixed population. We highlighted the basic factors influencing the transmission of Lassa fever and also determined and analyzed the important mathematical features of the model. We extended the model by introducing various control intervention measures, like external protection, isolation, treatment, and rodent control. The extended model was analyzed and compared with the basic model by appropriate qualitative analysis and numerical simulation approach. We invoked the optimal control theory so as to determine how to reduce the spread of the disease with minimum cost.
20 citations
TL;DR: The results show that a reduction in the number of contaminated workers and removal of contaminated food products are essential in eliminating the disease in the human population and vice versa and have significant public health implications in the management and containment of any listeriosis disease outbreak.
Abstract: Cross contamination that results in food-borne disease outbreaks remains a major problem in processed foods globally. In this paper, a mathematical model that takes into consideration cross contamination of Listeria monocytogenes from a food processing plant environment is formulated using a system of ordinary differential equations. The model has three equilibria: the disease-free equilibrium, Listeria-free equilibrium, and endemic equilibrium points. A contamination threshold is determined. Analysis of the model shows that the disease-free equilibrium point is locally stable for while the Listeria-free and endemic equilibria are locally stable for . The time-dependent sensitivity analysis is performed using Latin hypercube sampling to determine model input parameters that significantly affect the severity of the listeriosis. Numerical simulations are carried out, and the results are discussed. The results show that a reduction in the number of contaminated workers and removal of contaminated food products are essential in eliminating the disease in the human population and vice versa. The results have significant public health implications in the management and containment of any listeriosis disease outbreak.
19 citations
TL;DR: The result indicates that the disease dies out in areas with adequate preventive measures and widespread and kills more people in areaswith the inadequate preventive measures.
Abstract: The purpose of this study is to see whether it is possible to eradicate the disease theoretically using mathematical modeling with the aid of numerical simulation when disease occurs in a population by implementing adequate preventive measures. For this, we consider a mathematical model for the transmission dynamics of cholera and its preventive measure as one cohort of individuals, namely, a protected cohort in addition to susceptible, infected, and recovered cohorts of individuals including the concentration of Vibrio cholerae in the contaminated aquatic reservoir with small modifications. We calculate the basic reproduction number, , and investigate the existence and stability of equilibria. The model possessed forward bifurcation. Moreover, we compute the sensitivity indices of each parameter in relating to of the model. Numerical simulations are carried out to validate our theoretical results. The result indicates that the disease dies out in areas with adequate preventive measures and widespread and kills more people in areas with the inadequate preventive measures.
11 citations
TL;DR: Obtaining the exact solutions of the Jaulent–Miodek equation shows the simplicity, efficiency, and reliability of the used methods, which can be applied to other nonlinear partial differential equations taking place in mathematical physics.
Abstract: In this article, we utilize the - expansion method and the Jacobi elliptic equation method to analytically solve the (2 + 1)-dimensional integro-differential Jaulent–Miodek equation for exact solutions. The equation is shortly called the Jaulent–Miodek equation, which was first derived by Jaulent and Miodek and associated with energy-dependent Schrodinger potentials (Jaulent and Miodek, 1976; Jaulent, 1976). The equation is converted into a fourth order partial differential equation using a transformation. After applying a traveling wave transformation to the resulting partial differential equation, we obtain an ordinary differential equation which is the main equation to which the both schemes are applied. As a first step, the two methods give us distinguish systems of algebraic equations. The first method provides exact traveling wave solutions including the logarithmic function solutions of trigonometric functions, hyperbolic functions, and polynomial functions. The second approach provides the Jacobi elliptic function solutions depending upon their modulus values. Some of the obtained solutions are graphically characterized by the distinct physical structures such as singular periodic traveling wave solutions and peakons. A comparison between our results and the ones obtained from the previous literature is given. Obtaining the exact solutions of the equation shows the simplicity, efficiency, and reliability of the used methods, which can be applied to other nonlinear partial differential equations taking place in mathematical physics.
10 citations
TL;DR: Some fixed point results for generalized contraction in the framework of compete rectangular metric spaces are presented and some fixed point theorems for this type of mappings defined on such spaces are established.
Abstract: In this paper, we present some fixed point results for generalized contraction in the framework of compete rectangular metric spaces. Further, we establish some fixed point theorems for this type of mappings defined on such spaces. Our results generalize and improve many of the well-known results. Moreover, to support our main results, we give an illustrative example.
10 citations
TL;DR: A general formula is found that links the Wiener index with D -index of a regular graph G with different formulas of many special irregular graphs.
Abstract: For any two distinct vertices and in a connected graph , let be the length of path and the D –distance between and of is defined as: , where the minimum is taken over all paths and the sum is taken over all vertices of path . The D -index of G is defined as . In this paper, we found a general formula that links the Wiener index with D -index of a regular graph G . Moreover, we obtained different formulas of many special irregular graphs.
9 citations
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TL;DR: A continuous mathematical model of alcohol drinking with the influence of private and public addiction treatment centers shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium at alcohol present equilibrium.
Abstract: In this paper, we present a continuous mathematical model of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number . We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number . The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium when . When , drinking present equilibrium exists and the system is locally as well as globally asymptotically stable at alcohol present equilibrium .
8 citations
TL;DR: Findings showed that the effective use of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans have a significant impact in minimizing the disease spread in livestock and human populations.
Abstract: Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. The disease is of public health, veterinary, and economic significance in most of the developed and developing countries. Direct contact between susceptible and infective animals or their contaminated products are the two major routes of the disease transmission. In this paper, we investigate the impacts of controls of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans on the transmission dynamics of Brucellosis. The necessary conditions for an optimal control problem are rigorously analyzed using Pontryagin’s maximum principle. The main ambition is to minimize the spread of brucellosis disease in the community as well as the costs of control strategies. Findings showed that the effective use of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans have a significant impact in minimizing the disease spread in livestock and human populations. Moreover, cost-effectiveness analysis of the controls showed that the combination of livestock vaccination, gradual culling through slaughter, environmental sanitation, and personal protection in humans has high impact and lower cost of prevention.
8 citations
TL;DR: This paper proposes an effective and robust method for image alignment and recovery on a set of linearly correlated data via Frobenius and norms, which is more resilient to errors, outliers, and occlusions.
Abstract: This paper proposes an effective and robust method for image alignment and recovery on a set of linearly correlated data via Frobenius and norms. The most popular and successful approach is to model the robust PCA problem as a low-rank matrix recovery problem in the presence of sparse corruption. The existing algorithms still lack in dealing with the potential impact of outliers and heavy sparse noises for image alignment and recovery. Thus, the new algorithm tackles the potential impact of outliers and heavy sparse noises via using novel ideas of affine transformations and Frobenius and norms. To attain this, affine transformations and Frobenius and norms are incorporated in the decomposition process. As such, the new algorithm is more resilient to errors, outliers, and occlusions. To solve the convex optimization involved, an alternating iterative process is also considered to alleviate the complexity. Conducted simulations on the recovery of face images and handwritten digits demonstrate the effectiveness of the new approach compared with the main state-of-the-art works.
7 citations
TL;DR: An evacuation planning problem that aims to shift a maximum number of evacuees from a danger area to a safe zone in limited time under the budget constraints for network modification is considered and solution technique on static network is extended to the dynamic one.
Abstract: Many large-scale natural and human-created disasters have drawn the attention of researchers towards the solutions of evacuation planning problems and their applications. The main focus of these solution strategies is to protect the life, property, and their surroundings during the disasters. With limited resources, it is not an easy task to develop a universally accepted model to handle such issues. Among them, the budget-constrained network flow improvement approach plays significant role to evacuate the maximum number of people within the given time horizon. In this paper, we consider an evacuation planning problem that aims to shift a maximum number of evacuees from a danger area to a safe zone in limited time under the budget constraints for network modification. Different flow improvement strategies with respect to fixed switching cost will be investigated, namely, integral, rational, and either to increase the full capacity of an arc or not at all. A solution technique on static network is extended to the dynamic one. Moreover, we introduce the static and dynamic maximum flow problems with lane reversal strategy and also propose efficient algorithms for their solutions. Here, the contraflow approach reverses the direction of arcs with respect to the lane reversal costs to increase the flow value. As an implementation of an evacuation plan may demand a large cost, the solutions proposed here with budget constrained problems play important role in practice.
TL;DR: In this article, the authors give fundamental properties of groupoids such as uniqueness of inverses and properties of the identities and study subgroupoids, wide subgroupoid, and normal sub-groupoid.
Abstract: Using an algebraic point of view we present an introduction to the groupoid theory; that is, we give fundamental properties of groupoids as uniqueness of inverses and properties of the identities and study subgroupoids, wide subgroupoids, and normal subgroupoids. We also present the isomorphism theorems for groupoids and their applications and obtain the corresponding version of the Zassenhaus Lemma and the Jordan-Holder theorem for groupoids. Finally, inspired by the Ehresmann-Schein-Nambooripad theorem we improve a result of R. Exel concerning a one-to-one correspondence between partial actions of groups and actions of inverse semigroups.
TL;DR: A new robust regularized shrinkage regression method is proposed to recover and align high-dimensional images via affine transformation and Tikhonov regularization that surpasses to the baselines for image alignment and recovery relying on some public datasets.
Abstract: In this work, a new robust regularized shrinkage regression method is proposed to recover and align high-dimensional images via affine transformation and Tikhonov regularization. To be more resilient with occlusions and illuminations, outliers, and heavy sparse noises, the new proposed approach incorporates novel ideas affine transformations and Tikhonov regularization into high-dimensional images. The highly corrupted, distorted, or misaligned images can be adjusted through the use of affine transformations and Tikhonov regularization term to ensure a trustful image decomposition. These novel ideas are very essential, especially in pruning out the potential impacts of annoying effects in high-dimensional images. Then, finding optimal variables through a set of affine transformations and Tikhonov regularization term is first casted as mathematical and statistical convex optimization programming techniques. Afterward, a fast alternating direction method for multipliers (ADMM) algorithm is applied, and the new equations are established to update the parameters involved and the affine transformations iteratively in the form of the round-robin manner. Moreover, the convergence of these new updating equations is scrutinized as well, and the proposed method has less time computation as compared to the state-of-the-art works. Conducted simulations have shown that the new robust method surpasses to the baselines for image alignment and recovery relying on some public datasets.
TL;DR: This manuscript uses - weak contraction to generalize coincidence point results which are established in the context of partially ordered b-metric spaces and explicitly generalized some recent results from the existing literature.
Abstract: In this manuscript, we use - weak contraction to generalize coincidence point results which are established in the context of partially ordered b-metric spaces. The presented work explicitly generalized some recent results from the existing literature. Examples are also provided to show the authenticity of the established work.
TL;DR: A partial lane reversal approach in the class of multicommodity flow problems is introduced and a polynomial-time algorithm for the maximum static flow problem and pseudopolynomial algorithms for the earliest arrival transshipment and maximum dynamic flow problems are presented.
Abstract: The multicommodity flow problem arises when several different commodities are transshipped from specific supply nodes to the corresponding demand nodes through the arcs of an underlying capacity network. The maximum flow over time problem concerns to maximize the sum of commodity flows in a given time horizon. It becomes the earliest arrival flow problem if it maximizes the flow at each time step. The earliest arrival transshipment problem is the one that satisfies specified supplies and demands. These flow over time problems are computationally hard. By reverting the orientation of lanes towards the demand nodes, the outbound lane capacities can be increased. We introduce a partial lane reversal approach in the class of multicommodity flow problems. Moreover, a polynomial-time algorithm for the maximum static flow problem and pseudopolynomial algorithms for the earliest arrival transshipment and maximum dynamic flow problems are presented. Also, an approximation solution to the latter problem is obtained in polynomial-time.
TL;DR: The preliminary computational results for a set of 30 unconstrained optimization test problems show that this new spectral conjugate gradient outperforms a standard conjugates gradient in this field and the newly proposed spectral conjUGate gradient algorithm in bat algorithm is applied to reach the lowest possible goal of bat algorithm.
Abstract: Metaheuristic algorithms are used to solve many optimization problems. Firefly algorithm, particle swarm improvement, harmonic search, and bat algorithm are used as search algorithms to find the optimal solution to the problem field. In this paper, we have investigated and analyzed a new scaled conjugate gradient algorithm and its implementation, based on the exact Wolfe line search conditions and the restart Powell criterion. The new spectral conjugate gradient algorithm is a modification of the Birgin and Martinez method, a manner to overcome the lack of positive definiteness of the matrix defining the search direction. The preliminary computational results for a set of 30 unconstrained optimization test problems show that this new spectral conjugate gradient outperforms a standard conjugate gradient in this field and we have applied the newly proposed spectral conjugate gradient algorithm in bat algorithm to reach the lowest possible goal of bat algorithm. The newly proposed approach, namely, the directional bat algorithm (CG-BAT), has been then tested using several standard and nonstandard benchmarks from the CEC’2005 benchmark suite with five other algorithms and has been then tested using nonparametric statistical tests and the statistical test results show the superiority of the directional bat algorithm, and also we have adopted the performance profiles given by Dolan and More which show the superiority of the new algorithm (CG-BAT).
TL;DR: A new concept of - admissible almost type - contraction is introduced and some fixed point results for this new class of contractions in the context of complete metric spaces are proved.
Abstract: In this paper, we introduce a new concept of - admissible almost type - contraction and prove some fixed point results for this new class of contractions in the context of complete metric spaces. The presented results generalize and unify several existing results in the literature.
TL;DR: The asymptotic behavior of the two-dimensional quasi-geostrophic equations with subcritical dissipation is studied and it is established that vanishes at infinity.
Abstract: In this paper, we study the asymptotic behavior of the two-dimensional quasi-geostrophic equations with subcritical dissipation. More precisely, we establish that vanishes at infinity.
TL;DR: A set of convenient conditions of controllability for semilinear fractional finite dimensional control systems involving conformable fractional derivative and the iterative technique are established.
Abstract: In this paper, we establish a set of convenient conditions of controllability for semilinear fractional finite dimensional control systems involving conformable fractional derivative. Indeed, sufficient conditions of controllability for a semilinear conformable fractional system are presented, assuming that the corresponding linear systems are controllable. The present method is based on conformable fractional exponential matrix, Gramian matrix, and the iterative technique. Two illustrated examples are carried out to establish the facility and efficiency of this technique.
TL;DR: Numerical simulations that were carried out using the backward sweep method and Runge–Kutta scheme suggest that optimal controls under moderate and high scenarios can effectively reduce the cases of measles.
Abstract: This paper considers a deterministic model for the dynamics of measles transmission in a population divided into six classes with respect to the disease states: susceptible, vaccinated, exposed, infected, treated, and recovered. First, we investigate the dynamical properties of the SVEITR model such as its equilibrium points, their stability, and parameter sensitivity by applying constant controls. Criteria for determining the stability of disease-free and endemic equilibrium points are provided in terms of basic reproduction number. The model is then extended by incorporating vaccination, therapy, and treatment rates as time-dependent control variables representing the level of coverages. Application of Pontryagin’s maximum principle provides the necessary conditions that must be satisfied for the existence of optimal controls aiming at minimization of the number of exposed and infected individuals simultaneously with the control effort. Numerical simulations that were carried out using the backward sweep method and Runge–Kutta scheme suggest that optimal controls under moderate and high scenarios can effectively reduce the cases of measles. In particular, the moderate scenario that utilizes the existing coverage level of 86% for MCV1 and 69% for MCV2 can degrade the cost functional by 47% of the low scenario. Meanwhile, high scenario that takes the 2020 target of 96% as coverage only makes a slight difference in reducing the number of exposed and infected individuals.
TL;DR: The notions of nonself - contraction and - nonexpansive mappings are introduced, and a result showing the existence of best proximity point for every seminorm is shown.
Abstract: We consider the problem of best proximity point in locally convex spaces endowed with a weakly convex digraph. For that, we introduce the notions of nonself - contraction and - nonexpansive mappings, and we show that for each seminorm, we have a best proximity point. In addition, we conclude our work with a result showing the existence of best proximity point for every seminorm.
TL;DR: A deterministic mathematical model is formulated to study the transmission dynamics of bTB in humans and animals and shows that the disease decreases as the rate of consumption of dairy products decreases.
Abstract: Bovine tuberculosis (bTB) is a bacterial and zoonotic disease which is transmitted through consumption of unpasteurized milk and uncooked meat and inhalation of aerosols. In this paper, a deterministic mathematical model is formulated to study the transmission dynamics of bTB in humans and animals. The basic reproduction number R0 is computed to determine the behavior of the disease. Stability analysis shows that there is a possibility for disease-free equilibrium and endemic equilibrium to coexist when R0 = 1. To determine parameters which drive the dynamics of bTB, we performed sensitivity analysis. The analysis shows that the rate at which dairy products are produced, the rate of transmission of bTB from animal to animal, and the rates at which human acquires bTB from infectious dairy products and animals drive the transmission of bTB. However, the disease decreases as the rate of consumption of dairy products decreases. To control bTB, education campaign, inspection of dairy products, treatment of infected humans, and quarantine of infected animals are recommended.
TL;DR: A new reduction algorithm is presented for solving system of linear differential-algebraic equations with power series coefficients that would help to implement the manual calculations in commercial packages such as Mathematica, Maple, MATLAB, Singular, and Scilab.
Abstract: In this paper, we present a new reduction algorithm for solving system of linear differential-algebraic equations with power series coefficients. In the proposed algorithm, we transform the given system of differential-algebraic equations into another simple equivalent system using the elementary algebraic techniques. This algorithm would help to implement the manual calculations in commercial packages such as Mathematica, Maple, MATLAB, Singular, and Scilab. Maple implementation of the proposed algorithm is discussed, and sample computations are presented to illustrate the proposed algorithm.
TL;DR: The exact value of the reflexive vertex strength of any graph with pendant vertex is determined which is useful to analyse the reflexIVE vertex strength on sunlet graph, helm graph, subdivided star graph, and broom graph.
Abstract: A total - labeling is a function from the edge set to first natural number and a function from the vertex set to non negative even number up to , where . A vertex irregular reflexive -labeling of a simple, undirected, and finite graph is total - labeling, if for every two different vertices and of , , where . The minimum for graph which has a vertex irregular reflexive - labeling is called the reflexive vertex strength of the graph , denoted by . In this paper, we determined the exact value of the reflexive vertex strength of any graph with pendant vertex which is useful to analyse the reflexive vertex strength on sunlet graph, helm graph, subdivided star graph, and broom graph.
TL;DR: One modified MLR model combined with time series forecasting theory is presented and applied in grain consumption forecasting and the robustness of the model is verified by prediction analysis at different time intervals of historical data.
Abstract: In the classical multivariate prediction model, most research studies focused on the selection of relevant behaviour factors and the stability of historical data for improving the predicting accuracy of the main behaviour factor, and the historical data of the main behaviour factor have never been considered as one relevant behaviour factor, which in fact can be the first key impact factor; besides, the historical data can directly predict the main behaviour in the time series forecasting model, such as the ARIMA model. In this paper, one modified MLR model combined with time series forecasting theory is presented and applied in grain consumption forecasting. In the proposed model, to improve the current grain consumption forecasting, how to select impact factors is also discussed by combining the grey relational degree and Pearson correlation coefficient with given weights, and the optimal preprocessing parameter by the moving average filtering is computed for eliminating the abnormal points and stabilizing the data. Finally, the selected main impact factors are inputted to the proposed modified MLR model for forecasting grain consumption. Simulation results have shown that the five-year mean absolute percentage error of ration and feed grain is 2.34% and 3.27%, respectively, and the prediction accuracy has improved up to 2 times compared with the BP model and LSTM model. Moreover, the robustness of the model is verified by prediction analysis at different time intervals of historical data.
TL;DR: A mathematical model based on the predator-prey model with logistic growth, functional response, and the saturation effect that shows the possibility for the virus to be deactivated and blocked by the human immune system after they reach a certain value is introduced.
Abstract: We introduce a mathematical model that shows the interaction dynamics between the uninfected and the infected cancer cell populations with oncolytic viruses for the benign and the malignant cancer cases. There are two important parameters in our model that represent the malignancy level of the cancer cells and the efficacy of the therapy. The parameters play an important role to determine the possibility to have successful therapy for cancer. Our model is based on the predator-prey model with logistic growth, functional response, and the saturation effect that show the possibility for the virus to be deactivated and blocked by the human immune system after they reach a certain value. In this paper, we consider the appearance of the Hopf bifurcation on the system to characterize the treatment response based on the malignancy effect of the disease. We employ numerical bifurcation analysis when the value of the malignancy parameter is varied to understand the dynamics of the system.
TL;DR: This paper presents the notion of - contraction and - contraction in generalized asymmetric metric spaces to study the existence and uniqueness of the fixed point for them.
Abstract: In the last few decades, a lot of generalizations of the Banach contraction principle had been introduced. In this paper, we present the notion of - contraction and - contraction in generalized asymmetric metric spaces to study the existence and uniqueness of the fixed point for them. We will also provide some illustrative examples. Our results improve many existing results.
TL;DR: This paper derives the generalized Bayesian shrinkage estimator of parameter of Burr XII distribution under three loss functions: squared error, LINEX, and weighted balance loss functions.
Abstract: In this paper, we derive the generalized Bayesian shrinkage estimator of parameter of Burr XII distribution under three loss functions: squared error, LINEX, and weighted balance loss functions Therefore, we obtain three generalized Bayesian shrinkage estimators (GBSEs) In this approach, we find the posterior risk function (PRF) of the generalized Bayesian shrinkage estimator (GBSE) with respect to each loss function The constant formula of GBSE is computed by minimizing the PRF In special cases, we derive two new GBSEs under the weighted loss function Finally, we give our conclusion
TL;DR: The maximum likelihood and Bayes method and the Fisher information matrix have been used to obtain the estimating of the index Cpy for a 3-Burr-XII distribution based on Progressive Type-II censoring.
Abstract: In this paper, we discussed the estimation of the index for a 3-Burr-XII distribution based on Progressive Type-II censoring. The maximum likelihood and Bayes method have been used to obtain the estimating of the index . The Fisher information matrix has been used to construct approximate confidence intervals. Also, bootstrap confidence intervals (CIs) of the estimators have been obtained. The Bayesian estimates for the index have been obtained by the Markov Chain Monte Carlo method. Also, the credible intervals are constructed by using MCMC samples. Two real-datasets have been discussed using the proposed index.
TL;DR: Using the new iteration process, convergence and strong convergence theorems for the class of mappings satisfying the condition and the condition which is the generalization of Suzuki generalized nonexpansive mappings in the setting of hyperbolic spaces are proved.
Abstract: In this paper, we propose the generalized M-iteration process for approximating the fixed points from Banach spaces to hyperbolic spaces. Using our new iteration process, we prove - convergence and strong convergence theorems for the class of mappings satisfying the condition and the condition which is the generalization of Suzuki generalized nonexpansive mappings in the setting of hyperbolic spaces. Moreover, a numerical example is given to present the capability of our iteration process and the solution of the integral equation is also illustrated using our main result.