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Strong convergence for asymptotical pseudocontractions with the demiclosedness principle in banach spaces
Springer Science and Business Media LLC - Tập 2012 - Trang 1-8 - 2012
Yuan-Heng Wang, Yong-Hui Xia
The aim of this article is to give an answer to an interesting question proposed in Zhou. At the end of his article, he remarked that it was of great interest to extend his results to certain Banach spaces. So in this article, we extend the demiclosedness principle from Hilbert spaces to Banach spaces. A strong convergence theorem for asymptotical pseudo-contractions in Banach spaces is establishe...... hiện toàn bộ
A Note on Asymptotic Contractions
Springer Science and Business Media LLC - Tập 2007 - Trang 1-6 - 2006
Marina Arav, Francisco Eduardo Castillo Santos, Simeon Reich, Alexander J Zaslavski
We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space to converge to its unique fixed point, uniformly on each bounded subset of .
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
Applications of order-theoretic fixed point theorems to discontinuous quasi-equilibrium problems
Springer Science and Business Media LLC - - 2015
Congjun Zhang, Yuehu Wang
In this paper, we apply order-theoretic fixed point theorems and isotone selection theorems to study quasi-equilibrium problems. Some existence theorems of solutions to quasi-equilibrium problems are obtained on Hilbert lattices, chain-complete lattices and chain-complete posets, respectively. In contrast to many papers on equilibrium problems, our approach is order-theoretic and all results obtai...... 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
A new hybrid algorithm for a nonexpansive mapping
Springer Science and Business Media LLC - Tập 2015 - Trang 1-7 - 2015
Qiao-Li Dong, Yan-Yan Lu
In the paper, we introduce a new hybrid algorithm which is not based on the modification to weak convergence algorithms. The strong convergence theorem of the proposed algorithm is presented. Finally, the numerical experiments suggest that the new algorithm could be faster than Nakajo and Takahashi’s algorithm in J. Math. Anal. Appl. 279:372-379, 2003.
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.
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