A Viscosity Hybrid Steepest Descent Method for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems of Infinite Family of Strictly Pseudocontractive Mappings and Nonexpansive SemigroupReportar como inadecuado




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Abstract and Applied AnalysisVolume 2013 2013, Article ID 204948, 24 pages

Research ArticleSchool of Mathematics and Information Science, Weifang University, Weifang, Shandong 261061, China

Received 28 May 2013; Accepted 18 June 2013

Academic Editor: Sehie Park

Copyright © 2013 Haitao Che and Xintian Pan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, modifying the set of variational inequality and extending the nonexpansive mapping of hybrid steepest descent method to nonexpansive semigroups, we introduce a new iterative scheme by using the viscosity hybrid steepest descent method for finding a common element of the set of solutions of a system of equilibrium problems, the set of fixed points of an infinite family of strictly pseudocontractive mappings, the set of solutions of fixed points for nonexpansive semigroups, and the sets of solutions of variational inequality problems with relaxed cocoercive mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above sets under some mild conditions. The results shown in this paper improve and extend the recent ones announced by many others.





Autor: Haitao Che and Xintian Pan

Fuente: https://www.hindawi.com/



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