Showing papers by "Manuel De la Sen published in 2020"
TL;DR: The notion of Ciric type rational graphic Υ, Λ -contraction pair mappings is initiated and some new related common fixed point results on partial b-metric spaces endowed with a directed graph G are provided.
Abstract: In this paper, we initiate the notion of Ciric type rational graphic Υ , Λ -contraction pair mappings and provide some new related common fixed point results on partial b-metric spaces endowed with a directed graph G. We also give examples to illustrate our main results. Moreover, we present some applications on electric circuit equations and fractional differential equations.
54 citations
01 Jan 2020
TL;DR: In this article, a variant of discrete Jensen-type inequality for harmonic convex functions and a Jensen type equality for harmonic h-convex functions are presented, where h is the number of points in a convex function.
Abstract: In this article, we present a variant of discrete Jensen-type inequality for harmonic convex functions and establish a Jensen-type inequality for harmonic h-convex functions. Furthermore, we found a variant of Jensen-type inequality for harmonic h-convex functions.
31 citations
01 Mar 2020
TL;DR: In this article, the existence and uniqueness of fixed points for rational contractive mappings in complete metric-like spaces (dislocated metric spaces) were established and the results substantially generalize and extend several comparable results in the existing literature.
Abstract: In this paper, we introduce the notions of $$\alpha _{L}^{\psi }$$-rational contractive and cyclic $$\alpha _{L}^{\psi }$$- rational contractive mappings and establish the existence and uniqueness of fixed points for such mappings in complete metric-like spaces (dislocated metric spaces). The results presented here substantially generalize and extend several comparable results in the existing literature. As an application, we prove new fixed point results for $$\psi L$$-graphic and cyclic $$\psi L$$-graphic rational contractive mappings. Moreover, some examples and an application to integral equation are presented here to illustrate the usability of the obtained results.
27 citations
TL;DR: This paper studies an SIR (susceptible-infectious-recovered) epidemic model without demography and with no disease mortality under both total and under partial quarantine of the susceptible subpopulation or of both the susceptible and the infectious ones in order to satisfy the hospital availability requirements on bed disposal and other necessary treatment means for the seriously infectious subpopulations.
Abstract: This paper firstly studies an SIR (susceptible-infectious-recovered) epidemic model without demography and with no disease mortality under both total and under partial quarantine of the susceptible subpopulation or of both the susceptible and the infectious ones in order to satisfy the hospital availability requirements on bed disposal and other necessary treatment means for the seriously infectious subpopulations. The seriously infectious individuals are assumed to be a part of the total infectious being described by a time-varying proportional function. A time-varying upper-bound of those seriously infected individuals has to be satisfied as objective by either a total confinement or partial quarantine intervention of the susceptible subpopulation. Afterwards, a new extended SEIR (susceptible-exposed-infectious-recovered) epidemic model, which is referred to as an SEIAR (susceptible-exposed-symptomatic infectious-asymptomatic infectious-recovered) epidemic model with demography and disease mortality is given and focused on so as to extend the above developed ideas on the SIR model. A proportionally gain in the model parameterization is assumed to distribute the transition from the exposed to the infectious into the two infectious individuals (namely, symptomatic and asymptomatic individuals). Such a model is evaluated under total or partial quarantines of all or of some of the subpopulations which have the effect of decreasing the number of contagions. Simulated numerical examples are also discussed related to model parameterizations of usefulness related to the current COVID-19 pandemic outbreaks.
24 citations
21 Feb 2020
TL;DR: The main aim of as discussed by the authors is the investigation of possibilities for improvements and generalizations of the contractive condition of Ciric in the fuzzy metric spaces, and various versions of fuzzy contractive conditions are studied in two directions.
Abstract: The main aim of the current paper is the investigation of possibilities for improvements and generalizations contractive condition of Ciric in the fuzzy metric spaces. Various versions of fuzzy contractive conditions are studied in two directions. First, motivated by recent results, more general contractive conditions in fuzzy metric spaces are achieved and secondly, quasi-contractive type of mappings are investigated in order to obtain fixed point results with a wider class of t-norms.
23 citations
TL;DR: In this paper, the authors investigated a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies, i.e., vaccination of newborns and periodic impulsive vaccination on the susceptible.
Abstract: This paper investigates a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies. Firstly, the model is investigated under vaccination of newborns, which is fact in a direct action on the recruitment level of the model. Secondly, it is investigated under a periodic impulsive vaccination on the susceptible in the sense that the vaccination impulses are concentrated in practice in very short time intervals around a set of impulsive time instants subject to constant inter-vaccination periods. Both strategies can be adapted, if desired, to the time-varying levels of susceptible in the sense that the control efforts be increased as those susceptible levels increase. The model is discussed in terms of suitable properties like the positivity of the solutions, the existence and allocation of equilibrium points, and stability concerns related to the values of the basic reproduction number. It is proven that the basic reproduction number lies below unity, so that the disease-free equilibrium point is asymptotically stable for larger values of the disease transmission rates under vaccination controls compared to the case of absence of vaccination. It is also proven that the endemic equilibrium point is not reachable if the disease-free one is stable and that the disease-free equilibrium point is unstable if the reproduction number exceeds unity while the endemic equilibrium point is stable. Several numerical results are investigated for both vaccination rules with the option of adapting through ime the corresponding efforts to the levels of susceptibility. Such simulation examples are performed under parameterizations related to the current SARS-COVID 19 pandemic.
23 citations
TL;DR: In this paper, a new four-step iteration scheme for approximation of fixed point of the nonexpansive mappings named as - iteration scheme was introduced, which is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes.
Abstract: The purpose of this paper is to introduce a new four-step iteration scheme for approximation of fixed point of the nonexpansive mappings named as - iteration scheme which is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our proposed scheme. We present a numerical example to show that our iteration scheme is faster than the aforementioned schemes. Moreover, we present some weak and strong convergence theorems for Suzuki’s generalized nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve, and unify many existing results in the literature.
21 citations
TL;DR: It is found that one-third of the Indian population could eventually be infected by CO VID-19, and that a complete recovery from COVID-19 will happen only after an estimated 450 days from January 2020, and the SIR model suggests that the pandemic is likely to peak in India during the first week of November 2020.
Abstract: COVID-19 cases in India have been steadily increasing since January 30, 2020 and have led to a government-imposed lockdown across the country to curtail community transmission with significant impacts on societal systems. Forecasts using mathematical-epidemiological models have played and continue to play an important role in assessing the probability of COVID-19 infection under specific conditions and are urgently needed to prepare health systems for coping with this pandemic. In many instances, however, access to dedicated and updated information, in particular at regional administrative levels, is surprisingly scarce considering its evident importance and provides a hindrance for the implementation of sustainable coping strategies. Here we demonstrate the performance of an easily transferable statistical model based on the classic Holt-Winters method as means of providing COVID-19 forecasts for India at different administrative levels. Based on daily time series of accumulated infections, active infections and deaths, we use our statistical model to provide 48-days forecasts (28 September to 15 November 2020) of these quantities in India, assuming little or no change in national coping strategies. Using these results alongside a complementary SIR model, we find that one-third of the Indian population could eventually be infected by COVID-19, and that a complete recovery from COVID-19 will happen only after an estimated 450 days from January 2020. Further, our SIR model suggests that the pandemic is likely to peak in India during the first week of November 2020.
20 citations
02 Jan 2020
TL;DR: In this article, a generalized almost ( s, q ) − Jaggi F − Suzuki contraction type and some results in related fixed point on it in the context of b − metric-like spaces are discussed.
Abstract: The purpose of this article is to present a new generalized almost ( s , q ) − Jaggi F − contraction-type and a generalized almost ( s , q ) − Jaggi F − Suzuki contraction-type and some results in related fixed point on it in the context of b − metric-like spaces are discussed. Also, we support our theoretical results with non-trivial examples. Finally, applications to find a solution for the electric circuit equation and second-order differential equations are presented and an strong example is given here to support the first application.
20 citations
TL;DR: In this article, the existence of triple fixed points (TFPs) of a generalized nonlinear contraction mapping in complete cone b-metric spaces (CCbMSs) was proved.
Abstract: We prove the existence of tripled fixed points (TFPs) of a new generalized nonlinear contraction mapping in complete cone b-metric spaces (CCbMSs). Also, we present some exciting consequences as corollaries and three nontrivial examples. Finally, we find a solution for a tripled-system of integral equations (TSIE) and discussed a unique stationary distribution for the Markov process (SDMP).
17 citations
TL;DR: In this paper, the notion of C-type functions in partially ordered complete metric-like space (POCML space) was introduced to obtain triple coincidence points for non-self mappings.
Abstract: This manuscript aims to initiate some recent theoretical consequences related to tripled coincidence points for non-self mappings via the notion of C-type functions in partially ordered complete metric-like space (for short, POCML space) Our contributions unify and expand some previous studies in this line Moreover, some corollaries and suitable examples are presented to demonstrate the novelty of the results established Ultimately, two applications are given here to boost our theoretical consequences, the first one about the contributions of the integral type to obtain a triple coincidence points and the other application is about solving a system of nonlinear integral equations
TL;DR: The main goal in this manuscript is to accelerate the relaxed inertial Tseng-type (RITT) algorithm by adding a shrinking projection (SP) term to the algorithm by using a novel structure to solve an inclusion and a minimization problem under proper hypotheses.
Abstract: Our main goal in this manuscript is to accelerate the relaxed inertial Tseng-type (RITT) algorithm by adding a shrinking projection (SP) term to the algorithm. Hence, strong convergence results were obtained in a real Hilbert space (RHS). A novel structure was used to solve an inclusion and a minimization problem under proper hypotheses. Finally, numerical experiments to elucidate the applications, performance, quickness, and effectiveness of our procedure are discussed.
TL;DR: This work aims to use the power of artificial neural networks (ANN) to recognize the different incoming waves in order to distinguish the strong waves that provoke the stalling behavior and generate a suitable airflow speed reference for the airflow control scheme.
Abstract: Oscillating water column (OWC) plants face power generation limitations due to the stalling phenomenon. This behavior can be avoided by an airflow control strategy that can anticipate the incoming peak waves and reduce its airflow velocity within the turbine duct. In this sense, this work aims to use the power of artificial neural networks (ANN) to recognize the different incoming waves in order to distinguish the strong waves that provoke the stalling behavior and generate a suitable airflow speed reference for the airflow control scheme. The ANN is, therefore, trained using real surface elevation measurements of the waves. The ANN-based airflow control will control an air valve in the capture chamber to adjust the airflow speed as required. A comparative study has been carried out to compare the ANN-based airflow control to the uncontrolled OWC system in different sea conditions. Also, another study has been carried out using real measured wave input data and generated power of the NEREIDA wave power plant. Results show the effectiveness of the proposed ANN airflow control against the uncontrolled case ensuring power generation improvement.
TL;DR: This paper aims to present advanced algorithms arising out of adding the inertial technical and shrinking projection terms to ordinary parallel and cyclic hybrid inertial sub-gradient extra-gradient algorithms (for short, PCHISE).
Abstract: The paper aims to present advanced algorithms arising out of adding the inertial technical and shrinking projection terms to ordinary parallel and cyclic hybrid inertial sub-gradient extra-gradient algorithms (for short, PCHISE). Via these algorithms, common solutions of variational inequality problems (CSVIP) and strong convergence results are obtained in Hilbert spaces. The structure of this problem is to find a solution to a system of unrelated VI fronting for set-valued mappings. To clarify the acceleration, effectiveness, and performance of our parallel and cyclic algorithms, numerical contributions have been incorporated. In this direction, our results unify and generalize some related papers in the literature.
TL;DR: The notion of orthogonal F -metric spaces is presented and some fixed and periodic point theorems for Orthogonal ⊥ Ω -contraction are proved and the existence and uniqueness of the solution of a nonlinear fractional differential equation are proved.
Abstract: We present the notion of orthogonal F -metric spaces and prove some fixed and periodic point theorems for orthogonal ⊥ Ω -contraction. We give a nontrivial example to prove the validity of our result. Finally, as application, we prove the existence and uniqueness of the solution of a nonlinear fractional differential equation.
03 Jul 2020
TL;DR: This work establishes existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compares several well known iterative algorithms.
Abstract: We introduce a very general class of generalized non-expansive maps This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized α -non-expansive maps We establish some basic properties and demiclosed principle for this class of maps After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms
TL;DR: The main results in proving the existence and uniqueness of solution of nonlinear Barbashin-type integrodifferential equation satisfying a given initial value problem in modular metric space Xω are applied.
TL;DR: In this paper, the fixed points of multivalued quasi-none-expansive mappings were approximated via a faster iterative process and a faster fixed-point iterative method for finding the solution of two-point boundary value problems.
Abstract: In this paper, we approximate the fixed points of multivalued quasi-nonexpansive mappings via a faster iterative process and propose a faster fixed-point iterative method for finding the solution of two-point boundary value problems. We prove analytically and with series of numerical experiments that the Picard–Ishikawa hybrid iterative process has the same rate of convergence as the CR iterative process.
TL;DR: In this paper, the authors introduce Reich type contractions and ( )-contractions in the class of controlled metric spaces and establish some new related fixed point theorems, which are generalizations of some known results of literature.
Abstract: In this article, we introduce Reich type contractions and ( )- contractions in the class of controlled metric spaces and establish some new related fixed point theorems. Our results are generalizations of some known results of literature. Some examples and certain consequences are given to illustrate significance of presented results.
TL;DR: De la Sen and Ibeas as mentioned in this paper described and interpreted an SIR epidemic model through a logistic equation, which is parameterized by a Malthusian parameter and a carrying capacity parameter, both being time-varying, in general, and applied the model to the COVID-19 pandemic by using some recorded data.
Abstract: The main objective of this paper is to describe and interpret an SIR (Susceptible-Infectious-Recovered) epidemic model though a logistic equation, which is parameterized by a Malthusian parameter and a carrying capacity parameter, both being time-varying, in general, and then to apply the model to the COVID-19 pandemic by using some recorded data In particular, the Malthusian parameter is related to the growth rate of the infection solution while the carrying capacity is related to its maximum reachable value The quotient of the absolute value of the Malthusian parameter and the carrying capacity fixes the transmission rate of the disease in the simplest version of the epidemic model Therefore, the logistic version of the epidemics' description is attractive since it offers an easy interpretation of the data evolution especially when the pandemic outbreaks The SIR model includes recruitment, demography, and mortality parameters, and the total population minus the recovered population is not constant though time This makes the current logistic equation to be time-varying An estimation algorithm, which estimates the transmission rate through time from the discrete-time estimation of the parameters of the logistic equation, is proposed The data are picked up at a set of samples which are either selected by the adaptive sampling law or allocated at constant intervals between consecutive samples Numerical simulated examples are also discussed © 2020 Manuel De la Sen and Asier Ibeas
TL;DR: The modeling of an OWC and a rotational speed control using a novel Fuzzy Gain Scheduled-Sliding Mode controller for a stalling-free operation and results show the effectiveness of the proposed controls against the uncontrolled case and the superior performance of FGS-SMC over the SMC ensuring power generation improvement.
Abstract: The generated power of Oscillating Water Columns (OWC) based on Wells turbines is limited due to the stalling behavior. Therefore, this paper presents the modeling of an OWC and a rotational speed control using a novel Fuzzy Gain Scheduled-Sliding Mode controller (FGS-SMC) for a stalling-free operation. The proposed SMC-rotational speed control will regulate the turbo-generator angular velocity to avoid the stalling behavior and increase the generated power. In an effort to reduce the fluctuations in the generated power, Fuzzy Logic Supervisors (FLS) were designed to adaptively schedule the switching gains of the SMC controller to reduce the chattering and improve its performance. A comparative study has been carried out between the FGS-SMC, the SMC and uncontrolled OWC using irregular waves and real measured waves. Results show the effectiveness of the proposed controls against the uncontrolled case and the superior performance of FGS-SMC over the SMC ensuring power generation improvement.
TL;DR: This paper proves some escape time results for the generation of Julia and Madelbrot sets using a Picard Ishikawa type iterative process and discusses the effects of parameters on the color variation and shape of fractals.
Abstract: The aim of this paper is to present an application of a fixed point iterative process in generation of fractals namely Julia and Mandelbrot sets for the complex polynomials of the form T ( x ) = x n + m x + r where m , r ∈ C and n ≥ 2 . Fractals represent the phenomena of expanding or unfolding symmetries which exhibit similar patterns displayed at every scale. We prove some escape time results for the generation of Julia and Mandelbrot sets using a Picard Ishikawa type iterative process. A visualization of the Julia and Mandelbrot sets for certain complex polynomials is presented and their graphical behaviour is examined. We also discuss the effects of parameters on the color variation and shape of fractals.
TL;DR: This paper studies the representation of a general epidemic model by means of a first-order differential equation with a time-varying log-normal type coefficient and pays special attention to the evolution transients of the infection curve, rather than to the equilibrium points.
Abstract: This paper studies the representation of a general epidemic model by means of a first-order differential equation with a time-varying log-normal type coefficient. Then the generalization of the first-order differential system to epidemic models with more subpopulations is focused on by introducing the inter-subpopulations dynamics couplings and the control interventions information through the mentioned time-varying coefficient which drives the basic differential equation model. It is considered a relevant tool the control intervention of the infection along its transient to fight more efficiently against a potential initial exploding transmission. The study is based on the fact that the disease-free and endemic equilibrium points and their stability properties depend on the concrete parameterization while they admit a certain design monitoring by the choice of the control and treatment gains and the use of feedback information in the corresponding control interventions. Therefore, special attention is paid to the evolution transients of the infection curve, rather than to the equilibrium points, in terms of the time instants of its first relative maximum towards its previous inflection time instant. Such relevant time instants are evaluated via the calculation of an “ad hoc” Shannon’s entropy. Analytical and numerical examples are included in the study in order to evaluate the study and its conclusions.
01 Apr 2020
TL;DR: In this article, an extension of Darbo's fixed point theorem via θ -F-contractions in a Banach space has been presented, and a measure of noncompactness approach is the main tool in the presentation of their proofs.
Abstract: In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.
TL;DR: This paper introduces the new definition of the eventually Δ -restrictive set-valued map together with the concept of p-orbital continuity, and introduces another new concept called the Δ ( ϵ ) -restricting map, both of which provide us with schemes to find a fixed point.
Abstract: The symmetry concept is an intrinsic property of metric spaces as the metric function generalizes the notion of distance between two points. There are several remarkable results in science in connection with symmetry principles that can be proved using fixed point arguments. Therefore, fixed point theory and symmetry principles bear significant correlation between them. In this paper, we introduce the new definition of the eventually Δ -restrictive set-valued map together with the concept of p-orbital continuity. Further, we introduce another new concept called the Δ ( ϵ ) -restrictive set-valued map. We establish several fixed point results related to these maps and proofs of these results also provide us with schemes to find a fixed point. In a couple of results, the stronger condition of compactness of the underlying metric space is assumed. Some results are illustrated with examples.
31 Aug 2020
TL;DR: This paper introduced a new extragradient-like method to solve equilibrium problems in real Hilbert spaces with a Lipschitz-type condition on a bifunction and reported various numerical results to show the numerical behaviour of the proposed method and correlate it with existing ones.
Abstract: A plethora of applications from mathematical programming, such as minimax, and mathematical programming, penalization, fixed point to mention a few can be framed as equilibrium problems. Most of the techniques for solving such problems involve iterative methods that is why, in this paper, we introduced a new extragradient-like method to solve equilibrium problems in real Hilbert spaces with a Lipschitz-type condition on a bifunction. The advantage of a method is a variable stepsize formula that is updated on each iteration based on the previous iterations. The method also operates without the previous information of the Lipschitz-type constants. The weak convergence of the method is established by taking mild conditions on a bifunction. For application, fixed-point theorems that involve strict pseudocontraction and results for pseudomonotone variational inequalities are studied. We have reported various numerical results to show the numerical behaviour of the proposed method and correlate it with existing ones.
31 Aug 2020
TL;DR: Baloch et al. as discussed by the authors presented a variant of discrete Jensen-type inequality for harmonically convex functions, and then they proved the variant of Jensen type inequality for the harmonically h-convex functions.
Abstract: Discrete Jensen-type inequality for a harmonically convex function was established by Dragomir in [S. S. Dragomir, RGMIA Monographs, Victoria University, (2015)]. In [I. A. Baloch, A. H. Mughal, Y. M. Chu, M. De la Sen, Accepted in Aims Mathematics], Baloch et al. presented a variant of discrete Jensen-type inequality for harmonically convex functions. Moreover, they established a Jensen-type inequality for harmonically h-convex functions, and then they proved the variant of Jensen-type inequality for harmonically h-convex functions. Our results generalize and improve some earlier results in the literature (for example see [S. S. Dragomir, RGMIA Monographs, Victoria University, (2015)] and [I. A. Baloch, A. H. Mughal, Y. M. Chu, M. De la Sen, Accepted in Aims Mathematics]) for the said class. Additionally, using them gives us more interesting results.
TL;DR: The notions of orbitally continuous and asymptotically regular mappings in the set-valued context are newly extended to achieve this objective and two new existence of fixed point results corresponding to those inequalities are proved.
Abstract: The symmetry concept is a congenital characteristic of the metric function. In this paper, our primary aim is to study the fixed points of a broad category of set-valued maps which may include discontinuous maps as well. To achieve this objective, we newly extend the notions of orbitally continuous and asymptotically regular mappings in the set-valued context. We introduce two new contractive inequalities one of which is of Geraghty-type and the other is of Boyd and Wong-type. We proved two new existence of fixed point results corresponding to those inequalities.
TL;DR: In this paper, an ANN-based rotational speed control was proposed to avoid the stalling behavior in Oscillating Water Columns composed of a Doubly Fed Induction Generator driven by a Wells turbine.
Abstract: This paper presents an ANN-based rotational speed control to avoid the stalling behavior in Oscillating Water Columns composed of a Doubly Fed Induction Generator driven by a Wells turbine. This control strategy uses rotational speed reference provided by an ANN-based Maximum Power Point Tracking. The ANN-based MPPT predicts the optimal rotational speed reference from wave amplitude and period. The neural network has been trained and uses wave surface elevation measurements gathered by an acoustic Doppler current profiler. The implemented ANN-based rotational speed control has been tested with two different wave conditions and results prove the effectiveness of avoiding the stall effect which improved the power generation.
17 Mar 2020
TL;DR: The Suzuki-type ( α, β, γ g ) - generalized and modified proximal contractive mappings are introduced and fixed-point results in metric spaces and in partially ordered metric spaces are obtained.
Abstract: In this paper, we introduce Suzuki-type ( α , β , γ g ) - generalized and modified proximal contractive mappings. We establish some coincidence and best proximity point results in fairly complete spaces. Also, we provide coincidence and best proximity point results in partially ordered complete metric spaces for Suzuki-type ( α , β , γ g ) - generalized and modified proximal contractive mappings. Furthermore, some examples are presented in each section to elaborate and explain the usability of the obtained results. As an application, we obtain fixed-point results in metric spaces and in partially ordered metric spaces. The results obtained in this article further extend, modify and generalize the various results in the literature.