Showing papers in "Filomat in 2016"
TL;DR: In this article, the authors proposed a rapid and effective way of working out the optimum convergence control parameter in the homotopy analysis method (HAM) for solving algebraic, highly nonlinear differentialdifference, integro-differential, and ordinary or partial differential equations or systems.
Abstract: A rapid and effective way of working out the optimum convergence control parameter in the homotopy analysis method (HAM) is introduced in this paper. As compared with the already known ways of evaluating the convergence control parameter in HAM either through the classical constant h − curves ( h is the convergence control parameter) or from the classical squared residual error as frequently used in the literature, a novel description is proposed to find out an optimal value for the convergence control parameter yielding the same optimum values. In most cases, the new method is shown to perform quicker and better against the residual error method when integrations are much harder to evaluate. Examples involving solution of algebraic, highly nonlinear differentialdifference, integro-differential, and ordinary or partial differential equations or systems, all from the literature demonstrate the validity and usefulness of the introduced technique
115 citations
TL;DR: In this paper, a generalization of the Bleimann-Butzer-Hahn operators based on (p, q)-integers was introduced and the convergence of these operators was computed by using the modulus of continuity.
Abstract: In this paper, we introduce a generalization of the Bleimann-Butzer-Hahn operators based on (p,q)-integers and obtain Korovkin's type approximation theorem for these operators. Furthermore, we compute convergence of these operators by using the modulus of continuity.
89 citations
TL;DR: In this article, the authors present some fixed point results in the setting of complete metric spaces by defining a new contractive condition via admissible admissible mapping imbedded in simulation function.
Abstract: In this paper, we present some fixed point results in the setting of a
complete metric spaces by defining a new contractive condition via admissible
mapping imbedded in simulation function. Our results generalize and unify
several fixed point theorems in the literature.
68 citations
TL;DR: In this article, the existence of Ricci solitons on a Lorentzian para-Sasakian manifold was shown to imply that (M, φ, ξ, η, 1) is an elliptic manifold.
Abstract: We consider η-Ricci solitons on Lorentzian para-Sasakian manifolds satisfying certain curvature conditions: R(ξ,X) · S = 0 and S · R(ξ,X) = 0. We prove that on a Lorentzian para-Sasakian manifold (M, φ, ξ, η, 1), if the Ricci curvature satisfies one of the previous conditions, the existence of η-Ricci solitons implies that (M, 1) is Einstein manifold. We also conclude that in these cases there is no Ricci soliton on M with the potential vector field ξ. On the other way, if M is of constant curvature, then (M, 1) is elliptic manifold. Cases when the Ricci tensor satisfies different other conditions are also discussed.
67 citations
TL;DR: In this paper, a new three-step iteration scheme was introduced and convergence results for approximation of fixed points of nonexpansive mappings in the framework of Banach space were established.
Abstract: In this paper, we introduce a new three-step iteration scheme and establish convergence results for approximation of fixed points of nonexpansive mappings in the framework of Banach space. Further, we show that the new iteration process is faster than a number of existing iteration processes. To support the claim, we consider a numerical example and approximated the fixed point numerically by computer using Matlab.
66 citations
TL;DR: In this paper, an operator associated with generalized Mittag-Leffler function in the unit disk was introduced, and the virtue of differential subordination was used to obtain interesting results.
Abstract: The importance of Mitttag-Leffler function due to its involvement in many problems in natural and applied science. In this paper we introduce an operator associated with generalized Mittag-Leffler function in the unit disk U={z:|z|<1}. By using this operator and the virtue of differential subordination, we obtain interesting results. Some applications of our results are also obtained.
56 citations
TL;DR: A method of multi-criteria decision-making that combines simplified neutrosophic linguistic sets and normalized Bonferroni mean operator to address the situations where the criterion values take the form of simplified neutrophic linguistic numbers and the criterion weights are known.
Abstract: The main purpose of this paper is to provide a method of multi-criteria decision-making that combines simplified neutrosophic linguistic sets and normalized Bonferroni mean operator to address the situations where the criterion values take the form of simplified neutrosophic linguistic numbers and the criterion weights are known. Firstly, the new operations and comparison method for simplified neutrosophic linguistic numbers are defined and some linguistic scale functions are employed. Subsequently, a Bonferroni mean operator and a normalized weighted Bonferroni mean operator of simplified neutrosophic linguistic numbers are developed, in which some desirable characteristics and special cases with respect to the parameters and in Bonferroni mean operator are studied. Then, based on the simplified neutrosophic linguistic normalized weighted Bonferroni mean operator, a multi-criteria decision-making approach is proposed. Finally, an illustrative example is given and a comparison analysis is conducted between the proposed approach and other existing method to demonstrate the effectiveness and feasibility of the developed approach.
55 citations
TL;DR: In this paper, a new fractional integration formula involving the generalized multi-index Mittag-Leffler function was established, and an interesting special case of the main result was also considered.
Abstract: Recently Kiryakova and several other ones have investigated so-called multiindex Mittag-Leffler functions associated with fractional calculus. Here, in this paper, we aim at establishing a new fractional integration formula (of pathway type) involving the generalized multi-index Mittag-Leffler function $E_{\gamma, \kappa}[(\alpha_j,\beta_j)_m; z]$. An interesting special case of our main result is also considered.
45 citations
TL;DR: In this article, a lower bound for the harmonic index of a graph with minimum degree at least three is obtained and the corresponding extremal graph is characterized, where the degree of a vertex is defined as the sum of the weights of all vertices of the vertices in the graph.
Abstract: The harmonic index $H(G)$ of a graph $G$ is the sum of the weights $\frac{2}{d(u)+d(v)}$ of all edges $uv$ of $G$, where $d(u)$ denotes the degree of a vertex $u$ in $G$. In this work, a lower bound for the harmonic index of a graph with minimum degree at least three is obtained and the corresponding extremal graph is characterized.
40 citations
TL;DR: In this article, the relation between Zagreb polynomials of a graph and a graph obtained by applying the operators $S(G)$, $R(G), and $Q(G)) is investigated.
Abstract: In general, the relations among Zagreb polynomials on three graph operators are discussed in this paper. Specifically, relations between Zagreb polynomials of a graph $G$ and a graph obtained by applying the operators $S(G)$ , $R(G)$ and $Q(G)$ are investigated. In a separate section, the relation between Zagreb polynomial of a graph $G$ and its corona is also described.
33 citations
TL;DR: In this article, the Hermite-Hadamard type inequalities for fractional integrals were established for the first time, depending on a parameter of the integrals' complexity.
Abstract: In this paper, we have established Hermite-Hadamard type inequalities for
fractional integrals depending on a parameter.
TL;DR: This article introduces proximal relator spaces, a nonvoid family of proximity relations on a nonempty set that leads to an extension of fat and dense subsets of the relator space $X(\mathcal{R})$ to proximal fat and density subset of the space $\mathcal {R}_{delta}$.
Abstract: This article introduces proximal relator spaces. The basic approach is to define a nonvoid family of proximity relations $\mathcal{R}_{\delta}$ (called a proximal relator) on a nonempty set. The pair $(X,\mathcal{R}_{\delta})$ (also denoted $X(\mathcal{R}_{\delta})$) is called a proximal relator. Then, for example, the traditional closure of a subset of the Sz\'{a}z relator space $X(\mathcal{R})$ can be compared with the more recent descriptive closure of a subset of $X(\mathcal{R}_{\delta})$. This leads to an extension of fat and dense subsets of the relator space $X(\mathcal{R})$ to proximal fat and dense subsets of the space $\mathcal{R}_{\delta}$.
TL;DR: In this article, a general class of multivalued weakly Picard operators on complete metric space is given. And some illustrative examples showing that their results are proper generalizations of some previous theorems.
Abstract: In the present paper, considering a new concept of multivalued almost F-contraction, we give a general class of multivalued weakly Picard operators on complete metric space. Also, we give some illustrative examples showing that our results are proper generalizations of some previous theorems.
TL;DR: In this article, the authors used the collocation method based on the exponential cubic B-spline approximation together with the Crank Nicolson to solve the Kuramoto-Sivashinsky (KS) equation.
Abstract: In this study Kuramoto--Sivashinsky(KS) equation has been solved using the collocation method, based on the exponential cubic B-spline approximation together with the Crank Nicolson. The results of the proposed method are compared with both numerical and analytical results by studyinh two text probles.
TL;DR: The distribution of heavy metal concentrations in the beach sand samples collected from 44 different locations along the Manavgat-Alanya coastline of Antalya covering different coastal sandy beaches was studied as discussed by the authors.
Abstract: The distribution of heavy metal concentrations in the beach sand samples collected from 44 different locations along the Manavgat – Alanya coastline of Antalya covering different coastal sandy beaches was studied. The average concentration level of these metals in the beach sand was calculated and compared to those of the Earth Crust, Sandstone, Ultrabasic Rock and the acceptable limit for Turkey in order to determine their anomalies. Heavy metal (Cr, Zn, Ni, As, Cu, Pb, Co, Mo, Sb and Cd; along with Al, Fe, Mg, Mn, Na, K, Ba, Ca and W) were determined. The elements occurred in abundance as Ca> Na>Mg>Fe>Al>K>Ti>Mn>Cr>Ba>V>Zn>Ni>As>Cu>Pb>Co>Mo>Sb>W>Cd. The sufficiency of the number of samples used from the study area is revealed by the high explanatory power R 2 =96.9%, of the Model summary ANOVA. Using the box plot, it was also noted that some heavy metals such as As (in samples 1, 19, 25, 28 and 29); Mn (in Samples 23 and 39); Na (in samples 23, 24 and 45); Cr (in Sample 33) and Ti (in Sample 15)had very high anomalies. Heavy metal contents show high anomaly concentrations when compared to some background values (Earth Crust, Sandstone, Ultrabasic and Turkey acceptable limit).
TL;DR: In this article, various integral and convolution characterizations, coefficient estimates and differential subordination results for functions belonging to the class of functions in the open unit disk (U) of analytic functions are investigated.
Abstract: For $\alpha\in(\pi, \pi]$, let $\mathcal{R}_\alpha(\phi)$ denote the class of all normalized analytic functions in the open unit disk $\mathbb{U}$ satisfying the following differential subordination: $$f'(z)+\frac{1}{2}\left(1+e^{i\alpha}\right)zf''(z)\prec\phi(z)\qquad (z\in\mathbb{U}),$$ where the function $\phi(z)$ is analytic in the open unit disk $\mathbb{U}$ such that $\phi(0)=1$. In this paper, various integral and convolution characterizations, coefficient estimates and differential subordination results for functions belonging to the class $\mathcal{R}_\alpha(\phi)$ are investigated. The Fekete-Szeg\"{o} coefficient functional associated with the $k$th root transform $[f(z^k)]^{1/k}$ of functions in $\mathcal{R}_\alpha(\phi)$ is obtained. A similar problem for a corresponding class $\mathcal{R}_{\Sigma;\alpha}(\phi)$ of bi-univalent functions is also considered. Connections with previous known results are pointed out.
TL;DR: In this paper, the fractional optimal control problem for differential systems is considered in a Riemann-Liouville sense, and necessary and sufficient optimality conditions for fractional Dirichlet and Neumann problems with quadratic performance functional are derived.
Abstract: In this paper, the fractional optimal control problem for differential system is considered. The fractional time derivative is considered in a Riemann-Liouville sense. Constraints on controls are imposed. Necessary and sufficient optimality conditions for the fractional Dirichlet and Neumann problems with the quadratic performance functional are derived. Some examples are analyzed in detail.
Journal Article•
TL;DR: In this article, the authors employ the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions of nonlinear functional-integral equations.
Abstract: In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo’s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explain the generalizations and applications of our main result is also included.
TL;DR: In this article, the Faber polynomial expansions of the Taylor-Maclaurin coefficients of analytic bi-univalent functions were used to obtain bounds on the Taylor coefficients of the functions in this class.
Abstract: In this work, considering a general subclass of analytic bi-univalent functions, we determine estimates for the general Taylor-Maclaurin coefficients of the functions in this class. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coeffcient bounds.
TL;DR: In this paper, a new type of statistical product summability, statistical (C, 1) (E, 1 ) summability was introduced, and a rate of convergence which is uniform in Korovkin type theorem was shown.
Abstract: Korovkin-type approximation theory usually deals with convergence analysis for sequences of positive operators. This approximation theorem was extended to more general space of sequences via different way such as statistical convergence, summation processes. In this work, we introduce a new type of statistical product summability, that is, statistical (C,1) (E,1) summability and further apply our new product summability method to prove Korovkin type theorem. Furthermore, we present a rate of convergence which is uniform in Korovkin type theorem by statistical (C,1)(E,1) summability.
TL;DR: In this paper, the authors construct generating functions for the Jacobsthal polynomials and investigate properties of these polynomial families using their functional equations and infinite series applications.
Abstract: The purpose of this paper is to construct generating functions for the family of the Fibonacci and Jacobsthal polynomials. Using these generating functions and their functional equations, we investigate some properties of these polynomials. We also give relationships between the Fibonacci, Jacobsthal, Chebyshev polynomials and the other well known polynomials. Finally, we give some infinite series applications related to these polynomials and their generating functions.
TL;DR: In this article, the authors introduce the notions of $\alpha$-$F$-contractions, which are derived from fixed point theorems for multivalued mappings.
Abstract: In this paper, we introduce the notions of $\alpha$-$F$-contractions, by combining the notions of $\alpha$-$\psi$-contraction and $F$-contraction. Using our new notions we obtain some fixed point theorems for multivalued mappings. As an application we establish an existence theorem for integral equations. An example is also constructed to show an importance of our results.
TL;DR: By using Cauchy integral formula in the theory of complex functions, the authors established some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such as being operator monotone function, being complete Bernstein function, and being Stieltjes function.
Abstract: By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such as being operator monotone function, being complete Bernstein function, and being Stieltjes function, for these functions, and verify a conjecture on complete monotonicity of a function involving the logarithmic function.
TL;DR: Wang et al. as discussed by the authors investigated the analytic hierarchy process (AHP) as a method of measuring index weights for group decision-making (GDM), taking into full account the cognitive levels of different experts.
Abstract: Credit risk analysis is a core research issue in the field of financial risk
management. This paper first investigates the analytic hierarchy process
(AHP) as a method of measuring index weights for group decision-making (GDM).
AHP for group decision-making (AHP-GDM) is then researched and applied,
taking into full account the cognitive levels of different experts. Second,
the concept of grey relational degree is introduced into the ideal solution
of the technique for order of preference by similarity to ideal solution
(TOPSIS). This concept fully considers the relative closeness of grey
relational degree between alternatives and the ”ideal” solution in order to
strengthen their relationship. The AHP-GDM method overcomes the problem of
subjectivity in measuring index weights, and the revised TOPSIS (R-TOPSIS)
method heightens the effectiveness of assessment results. An illustrative
case using data from Chinese listed commercial banks shows that the R-TOPSIS
method is more effective than both TOPSIS and grey relational analysis (GRA)
in credit risk evaluation. The two improved multi-criteria decision making
(MCDM) methods are also applied to empirical research regarding the credit
risk analysis of Chinese urban commercial banks. The results indicate the
validity and effectiveness of both methods.
TL;DR: In this paper, a discrete Sturm-Liouville problem with Dirichlet boundary conditions is considered and it is shown that the specication of the eigenvalues and weight numbers uniquely determines the potential.
Abstract: We consider a discrete Sturm{Liouville problem with Dirichlet boundary conditions. We show that the specication of the eigenvalues and weight numbers uniquely determines the potential. Moreover, we also show that if the potential is symmetric, then it is uniquely determined by the specication of the eigenvalues. These are discrete versions of well-known results for corresponding dierential equations.
TL;DR: In this paper, a very close connection between hyperbolicity and chordality has been found between edge-chordality and Gromov-hyperbolic properties of graphs.
Abstract: If X is a geodesic metric space and $x_1,x_2,x_3\in X$, a {\it geodesic triangle} $T=\{x_1,x_2,x_3\}$ is the union of the three geodesics $[x_1x_2]$, $[x_2x_3]$ and $[x_3x_1]$ in $X$. The space $X$ is $\delta$-\emph{hyperbolic} $($in the Gromov sense$)$ if any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides, for every geodesic triangle $T$ in $X$. An important problem in the study of hyperbolic graphs is to relate the hyperbolicity with some classical properties in graph theory. In this paper we find a very close connection between hyperbolicity and chordality: we extend the classical definition of chordality in two ways, edge-chordality and path-chordality, in order to relate this property with Gromov hyperbolicity. In fact, we prove that every edge-chordal graph is hyperbolic and that every hyperbolic graph is path-chordal. Furthermore, we prove that every path-chordal cubic graph with small path-chordality constant is hyperbolic.
TL;DR: In this article, the authors studied the short-time Fourier transform on the space of distributions of exponential type and obtained various Tauberian theorems for the Fourier Transform.
Abstract: We study the short-time Fourier transform on the space $\mathcal{K}_{1}'(\mathbb{R}^n)$ of distributions of exponential type. We give characterizations of $\mathcal{K}_{1}'(\mathbb{R}^n)$ and some of its subspaces in terms of modulation spaces. We also obtain various Tauberian theorems for the short-time Fourier transform.
TL;DR: In this article, a modified Noor iterative method in a convex metric space and apply it to approximate fixed points of quasi-contractive operators introduced by Berinde et al.
Abstract: We introduce modified Noor iterative method in a convex metric space and apply it to approximate fixed points of quasi-contractive operators introduced by Berinde \cite {Berinde(2005-2)}. Our results generalize and improve upon, among others, the corresponding results of Berinde \cite {Berinde(2005-2)}, Bosede \cite {Bosede} and Phuengrattana and Suantai \cite {Phu- Suantai}. We also compare the rate of convergence of proposed iterative method to the iterative methods due to Noor \cite {XuNoor}, Ishikawa \cite {Ishikawa} and Mann \cite {Mann}. It has been observed that the proposed method is faster than the other three methods. Incidently the results obtained herein provide analogues of the corresponding results of normed spaces and holds in $CAT(0)$ spaces, simultaneously.
TL;DR: In this paper, a new class of analytic and $p$-valent functions involving higher-order derivatives was introduced and studied, and several interesting properties including coefficient inequalities, distortion theorems, extreme points, and radii of close-to-convexity, starlikeness and convexity were derived.
Abstract: In this paper we introduce and study a new class of analytic and $p$-valent functions involving higher-order derivatives. For this $p$-valent function class, we derive several interesting properties including (for example) coefficient inequalities, distortion theorems, extreme points, and the radii of close-to-convexity, starlikeness and convexity. Several applications involving an integral operator are also considered. Finally, we obtain some results for the modified Hadamard product of the functions belonging to the $p$-valent function class which is introduced here.
TL;DR: In this paper, the Hermite-Hadamard type inequalities for differentiable functions are established and several applications for special means are given as well; see Section 2.1.
Abstract: In this paper, we establish some new Hermite-Hadamard-type inequalities for differentiable functions. Several applications for special means are given as well.