Strong convergence theorems for fixed point problems of a nonexpansive semigroup in a Banach space

Author:

Wang Xin,Hu Changsong,Guan Jinlin

Abstract

Abstract In this paper, we study the implicit and explicit viscosity iteration schemes for a nonexpansive semigroup in a reflexive, strictly convex and uniformly smooth Banach space which satisfies Opial’s condition. Our results improve and generalize the corresponding results given by Yao et al. (Fixed Point Theory Appl. 2013, doi:10.1186/1687-1812-2013-31) and many others. MSC:47H05, 47H10, 47H17.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Geometry and Topology

Reference15 articles.

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2. Sunthrayuth P, Kumam P: A general iterative algorithm for the solution of variational inequalities for a nonexpansive semigroup in Banach spaces. J. Nonlinear Anal. Optim. 2010, 1: 139–150.

3. Yao, Y, Liou, Y-C, Yao, J-C: Algorithms for finding minimum norm solution of equilibrium and fixed point problems for nonexpansive semigroups in Hilbert spaces. J. Nonlinear Convex Anal. (in press)

4. Yang P, Yao Y, Liou Y-C, Chen R: Hybrid algorithms of nonexpansive semigroups for variational inequalities. J. Appl. Math. 2012. 10.1155/2012/634927

5. Yao Y, Cho YJ, Liou Y-C: Hierarchical convergence of an implicit double-net algorithm for nonexpansive semigroups and variational inequalities. Fixed Point Theory Appl. 2011., 2011: Article ID 101 10.1186/1687-1812-2011-101

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