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Fixed point theorems in a new type of modular metric spaces
Springer Science and Business Media LLC - Tập 2018 - Trang 1-10 - 2018
Duran Turkoglu, Nesrin Manav
In this paper, considering both a modular metric space and a generalized metric space in the sense of Jleli and Samet (Fixed Point Theory Appl. 2015:61, 2015), we introduce a new concept of generalized modular metric space. Then we present some examples showing that the generalized modular metric space includes some kind of metric structures. Finally, we provide some fixed point results for both c...... hiện toàn bộ
Generalized proximal-type methods for weak vector variational inequality problems in Banach spaces
Springer Science and Business Media LLC - Tập 2015 - Trang 1-14 - 2015
Lin-chang Pu, Xue-ying Wang, Zhe Chen
In this paper, we propose a class of generalized proximal-type method by the virtue of Bregman functions to solve weak vector variational inequality problems in Banach spaces. We carry out a convergence analysis on the method and prove the weak convergence of the generated sequence to a solution of the weak vector variational inequality problems under some mild conditions. Our results extend some ...... hiện toàn bộ
Strong convergence of viscosity approximation methods for the fixed-point of pseudo-contractive and monotone mappings
Springer Science and Business Media LLC - Tập 2013 - Trang 1-11 - 2013
Yan Tang
In this paper, we introduce a viscosity iterative process, which converges strongly to a common element of the set of fixed points of a pseudo-contractive mapping and the set of solutions of a monotone mapping. We also prove that the common element is the unique solution of certain variational inequality. The strong convergence theorems are obtained under some mild conditions. The results presente...... hiện toàn bộ
Strong convergence theorems of nonlinear operator equations for countable family of multi-valued total quasi-ϕ-asymptotically nonexpansive mappings with applications
Springer Science and Business Media LLC - Tập 2012 - Trang 1-17 - 2012
Shih-Sen Chang, Lin Wang, Yong-Kun Tang, Yun-He Zhao, Zao-Li Ma
The purpose of this article is first to introduce the concept of total quasi-ϕ-asymptotically nonexpansive multi-valued mapping which contains many kinds of mappings as its special cases, and then by using the hybrid shrinking technique to propose an iterative algorithm for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variat...... hiện toàn bộ
Convergence theorems for finite families of total asymptotically nonexpansive mappings in hyperbolic spaces
Springer Science and Business Media LLC - Tập 2016 - Trang 1-13 - 2016
Bashir Ali
In this paper, using a multistep iterative scheme, we establish strong and Δ-convergence theorems for finite families of total asymptotically quasi-nonexpansive mappings in uniformly convex hyperbolic spaces. We then establish Δ- and polar convergence theorems for finite families of total asymptotically nonexpansive mappings in CAT(0) spaces. These new theorems are extensions, improvements, and ge...... hiện toàn bộ
Some results on zero points of m-accretive operators in reflexive Banach spaces
Springer Science and Business Media LLC - - 2014
Chang Qun Wu, Songtao Lv, Yunpeng Zhang
Abstract A modified proximal point algorithm is proposed for treating common zero points of a finite family of m-accretive operators. A strong convergence theorem is established in a reflexive, strictly convex Banach space with the uniformly Gâteaux differentiable norm.
Fixed point theorems and endpoint theorems for $(\alpha,\psi)$ -Meir-Keeler-Khan multivalued mappings
Springer Science and Business Media LLC - Tập 2016 - Trang 1-18 - 2016
Zhigang Wang, Huilai Li
As an extension of the class of $(\alpha,\psi)$ -Meir-Keeler-Khan single-valued mappings defined by Redjel et al., a new type of ...... hiện toàn bộ
Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions
Springer Science and Business Media LLC - Tập 2008 - Trang 1-9 - 2008
Liang-Gen Hu, Ti-Jun Xiao, Jin Liang
This paper concerns common fixed points for a finite family of hemicontractions or a finite family of strict pseudocontractions on uniformly convex Banach spaces. By introducing a new iteration process with error term, we obtain sufficient and necessary conditions, as well as sufficient conditions, for the existence of a fixed point. As one will see, we derive these strong convergence theorems in ...... hiện toàn bộ
Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators
Springer Science and Business Media LLC - - 2014
Hudson Akewe, Godwin Amechi Okeke, Adekunle F. Olayiwola
Modified block iterative procedure for solving the common solution of fixed point problems for two countable families of total quasi-ϕ-asymptotically nonexpansive mappings with applications
Springer Science and Business Media LLC - Tập 2012 - Trang 1-23 - 2012
Pongrus Phuangphoo, Poom Kumam
In this paper, we introduce a new iterative procedure which is constructed by the modified block hybrid projection method for solving a common solution of fixed point problems for two countable families of uniformly total quasi-ϕ-asymptotically nonexpansive and uniformly Lipschitz continuous mappings. Under suitable conditions, some strong convergence theorems are established in a uniformly smooth...... hiện toàn bộ
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