Strong convergence of implicit and explicit iterations for a class of variational inequalities in Banach spaces
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Authors
Lu-Chuan Ceng
- Department of Mathematics, Shanghai Normal University, Shanghai 200234, China.
Ching-Feng Wen
- Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80702, Taiwan.
- Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80702, Taiwan.
Abstract
In this paper, we introduce and analyze implicit and explicit iteration methods for solving a variational inequality problem
over the set of common fixed points of an infinite family of nonexpansive mappings on a real reflexive and strictly convex Banach
space with a uniformly Gâteaux differentiable norm. Strong convergence results are given. Our results improve and extend the
corresponding results in the literature.
Share and Cite
ISRP Style
Lu-Chuan Ceng, Ching-Feng Wen, Strong convergence of implicit and explicit iterations for a class of variational inequalities in Banach spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3502--3518
AMA Style
Ceng Lu-Chuan, Wen Ching-Feng, Strong convergence of implicit and explicit iterations for a class of variational inequalities in Banach spaces. J. Nonlinear Sci. Appl. (2017); 10(7):3502--3518
Chicago/Turabian Style
Ceng, Lu-Chuan, Wen, Ching-Feng. "Strong convergence of implicit and explicit iterations for a class of variational inequalities in Banach spaces." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3502--3518
Keywords
- Nonexpansive mapping
- fixed point
- variational inequality
- global convergence.
MSC
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