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In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper, we present a explicit viscosity technique of nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorem of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this paper extend and improve some recent announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper, we present a explicit viscosity technique of nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorem of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this paper extend and improve some recent announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the generalized viscosity implicit rules of one asymptotically nonexpansive mapping in Hilbert spaces. We obtain some strong convergence theorems under certain assumptions imposed on the parameters. We also apply our main results to solve mixed equilibrium problem in Hilbert spaces. A numerical example is also given to support our main results. The results obtained in this paper improve and extend many recent ones in this field. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a class of new general iteration processes for two finite families of total asymptotically nonexpansive mappings in hyperbolic spaces, which includes asymptotically nonexpansive mapping, (generalized) nonexpansive mapping of all normed linear spaces, Hadamard manifolds and CAT(0) spaces as special cases. Some important related properties to the new general iterative processes are also given and analyzed, and Δ-convergence and strong convergence of the iteration in hyperbolic spaces are proved. Furthermore, some meaningful illustrations for clarifying our results and two open questions are proposed. The results presented in this paper extend and improve the corresponding results announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, an uncountable infinite family of nonlinear mappings are investigated. Strong convergence theorems of common solutions are established in a strictly convex and uniformly smooth Banach space which also has the Kadec-Klee property. The results obtained in this paper unify and improve many corresponding results announced recently. [ABSTRACT FROM AUTHOR]

In this paper, based on the work by Moudafi and inspired by Takahashi and Xu, we try to investigate the split common fixed point problems for the class of demicontractive mappings in the setting of two Banach spaces, and obtain the strong and weak convergence theorems. The results presented in the paper improve and extend some recent well-known corresponding results. [ABSTRACT FROM AUTHOR]

In this paper, based on the work by Moudafi and inspired by Takahashi and Xu, we try to investigate the split common fixed point problems for the class of demicontractive mappings in the setting of two Banach spaces, and obtain the strong and weak convergence theorems. The results presented in the paper improve and extend some recent well-known corresponding results. [ABSTRACT FROM AUTHOR]

In this paper, an uncountable infinite family of nonlinear mappings are investigated. Strong convergence theorems of common solutions are established in a strictly convex and uniformly smooth Banach space which also has the Kadec-Klee property. The results obtained in this paper unify and improve many corresponding results announced recently. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concept of total asymptotically nonexpansive mappings and to prove some Δ-convergence theorems of iteration processes with errors to approximating a common fixed point for four total asymptotically nonexpansive mappings in hyperbolic spaces. The results presented in the paper extend and improve some recent results announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S-metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the the- oretical results, we also present some illustrative examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the notion of Meir-Keeler contraction condition in Mb-metric spaces. We prove some fixed point theorems for this class of contractions which enables us to extend and generalize the recent results of Gholmian and Khanehgir [2]. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper, we discuss the convergence theorems for the double acting iterative scheme to a common fixed point for a family of generalized Φ-weak contraction mappings in CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the stability of the Cauchy-Jensen and bi-quadratic functional equation... respectively, in 2-Banach spaces. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of continuous selection of a multivalued mapping in product space. Many authors provided existence of continuous map for lower semicontinuous. We provide continuous selection for weakly lower semicontinuous. Rhybinski [9] proved the existence for contraction type mapping. We prove the existence for some general type of mapping different from contraction mapping. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to study the existence of solution of a system of differential equations using fixed point technique. In this regard, in the first part of this article, along with some properties of partial b-metric topology, we prove a common fixed point theorem for generalized Geraghty type contraction mappings in a complete partial b-metric spaces. Then in second part we apply this result to show the existence of the solution of a system of ordinary differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and consider a new generalized system of nonlinear mixed variational inequality involving three difference relaxed cocoercive operators. This work is to use the resolvent operator technique to find the common solutions for a new generalized system of relaxed cocoercive mixed variational inequality problems and fixed point problems for Lipschitz mappings in Hilbert spaces. Our result in this paper improves and generalizes some know corresponding results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and consider a new generalized system of nonlinear mixed variational inequality involving three difference relaxed cocoercive operators. This work is to use the resolvent operator technique to find the common solutions for a new generalized system of relaxed cocoercive mixed variational inequality problems and fixed point problems for Lipschitz mappings in Hilbert spaces. Our result in this paper improves and generalizes some know corresponding results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove a strong convergence theorem for finding a common solutions of a general system of variational inequalities involving two different inverse-strongly accretive operators and solutions of fixed point problems involving the nonexpansive mapping in a Banach space by using a modified viscosity extragradient method with weak contraction. Moreover, using the above results, we can apply to finding solutions of zeros of accretive operators and the class of k-strictly pseudocontractive mappings. The results presented in this paper extend and improve the corresponding results of Qin et al. [Convergence of an iterative algorithm for systems of variational inequalities and nonexpansive mappings with applications, J. Comput. Appl. Math., 233 (2009), 231-240.], Aoyama et al. [Weak convergence of an iterative sequence for accretive operators in Banach spaces, Fixed Point Theory and Applications, vol. 2006, Article ID 35390, 1-13.], Yao et al. [Modified extragradient methods for a system of variational inequalities in Banach spaces, Acta. Appl. Math., 110(3) (2010), 1211-1224.], Katchang et al. [A viscosity iterative scheme for inverse-strongly accretive operators in Banach spaces, Journal of Computational Analysis and Applications, 12(3) (2010), 678 686.] and many others. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the random nonlinear variational inclusion problem with multi-valued random operators. We define a random iterative algorithm for finding the approximate solutions of class of random variational inclusions and establish the convergence of random iterative sequence generated by proposed algorithm in a uniformly smooth Banach space. Our result in this paper improves and generalizes some know corresponding results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the mapping satisfying mixed g-monotone property in partially ordered complete Menger probabilistic G-metric spaces. By weakening the notion of Ψ, we prove some new coupled coincidence point theorems and coupled common fixed point theorems. Finally, we provide an example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of differentiability and gradient for fuzzy mappings are presented and discussed using the characteristic theorem for generalized difference of n dimensional fuzzy numbers. The relationships of gradient, support-function-wise gradient and level-wise gradient are characterized. [ABSTRACT FROM AUTHOR]

In this paper, a concept of C*-algebra-valued modular metric space is introduced which is a generalization of a modular metric space of Chistyakov (Folia Math. 14 (2008), 3-25). Next, some common fixed point theorems are proved for generalized contraction type mappings on such spaces. Also, to support of our results an application is provided for existence and uniqueness of solution for a system of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new extragradient method with regularization for finding a common element of the solution set Γ of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in infinitedimensional Hilbert spaces, combining the regularization method and the technique of averaged operator, we prove the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)∩Γ under mild conditions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of common fixed point for three mappings in Gb-complete Gb-metric space. On the other hand, we prove that the theory is also established in G-metric space and several corollaries and examples are listed. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S-metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the the- oretical results, we also present some illustrative examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of continuous selection of a multivalued mapping in product space. Many authors provided existence of continuous map for lower semicontinuous. We provide continuous selection for weakly lower semicontinuous. Rhybinski [9] proved the existence for contraction type mapping. We prove the existence for some general type of mapping different from contraction mapping. [ABSTRACT FROM AUTHOR]

The purpose of this paper, we discuss the convergence theorems for the double acting iterative scheme to a common fixed point for a family of generalized φ-weak contraction mappings in CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of fixed points for Kannan contraction, Chat- terjea contraction and Reich contraction in setting of digital metric spaces. These digital con-tractions are the applications of metric fixed point theory contractions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new idea of best proximity point of F-contraction on a closed ball and obtain new theorems in a complete metric space. That is why this outcome becomes useful for contraction of a mapping on a closed ball instead of the whole space. At the same time, some comparative examples are constructed which establish the superiority of our results. Our results that have come into being give a proof of extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a viscosity rule for common fixed points of two non-expansive mappings in Hilbert spaces. The strong convergence of this technique is proved under certain assumptions imposed on the sequence of parameters. [ABSTRACT FROM AUTHOR]

In this paper, some notions are introduced in modular metric spaces. Next some common fixed points are established in ω-orbitally complete modular metric spaces by employing C-class functions that extend and generalize the results of [10, 18]. Finally, for usibility of our results an application is provided to show the existence of solutions for certain system of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some coupled fixed point results for two mappings satisfying some contractive conditions in cone b-metric spaces over Banach algebras with a solid cone by virtue of the properties of spectral radius. Also we give an example as an applications of one of the main results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study a class of new two-step viscosity iteration methods for approximating fixed points of set-valued nonexpansive mappings in CAT(0) spaces. Here, the fixed point is unique solution of a variational inequality with a contraction mapping. Further, we prove strong convergence theorem of the two-step viscosity iterations with some general conditions in a complete CAT(0) space. The presented results improve and unify the corresponding results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we present some properties of dual partial metric (abbreviation, pmetric) topology and investigate a fixed point result for self mappings in dual pmetric space. This result gener-alizes Banach contraction principle in a different way than in the known results from the literature. The article includes an example which shows the validity of our result. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to characterize the conditions for the convergence of the iterative scheme in the sense of Alghamdi et al. [The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014), Article ID 96, 9 pages] associated with Φ-hemicontractive mappings in a nonempty convex subset of an arbitrary Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces [ABSTRACT FROM AUTHOR]

This paper deals with the existence of continuous selection of a multivalued mapping in product space. Many authors provided existence of continuous map for lower semicontinuous. We provide continuous selection for weakly lower semicontinuous. Rhybinski [9] proved the existence for contraction type mapping. We prove the existence for some general type of mapping different from contraction mapping. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S-metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the the- oretical results, we also present some illustrative examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new idea of best proximity point of F-contraction on a closed ball and obtain new theorems in a complete metric space. That is why this outcome becomes useful for contraction of a mapping on a closed ball instead of the whole space. At the same time, some comparative examples are constructed which establish the superiority of our results. Our results that have come into being give a proof of extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a viscosity rule for common fixed points of two non-expansive mappings in Hilbert spaces. The strong convergence of this technique is proved under certain assumptions imposed on the sequence of parameters. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some coupled fixed point results for two mappings satisfying some contractive conditions in cone 6-metric spaces over Banach algebras with a solid cone by virtue of the properties of spectral radius. Also we give an example as an applications of one of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we present some properties of dual partial metric (abbreviation, pmetric) topology and investigate a fixed point result for self mappings in dual pmetric space. This result generalizes Banach contraction principle in a different way than in the known results from the literature. The article includes an example which shows the validity of our result. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish some common fixed point theorems for two pairs of self mappings in dislocated metric spaces which generalize, extend, and improve related results in the literature. Some applications of new results are provided. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce several types of Meir-Keeler contractive mappings in the structure of Ms-metric spaces. Then we study some existence and uniqueness fixed point theorems for these types of MKC mappings in Ms-metric spaces via Gupta-Saxena type contraction and other fraction version type contractions. Also, we extend and improve very recent results in fixed point theory. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of a fixed point of a self-mapping T on a Menger PM-space under two constraint inequalities with respect to two partial orders under two kinds of contractive conditions and obtain some new fixed point results. We then present several useful consequences of our main results. We also give examples to show the validity of our main results. [ABSTRACT FROM AUTHOR]