A System of Generalized Mixed Equilibrium Problems and Fixed Point Problems for Pseudocontractive Mappings in Hilbert Spaces

Fixexd point theory and applications

Poom Kumam²  Chaichana Jaiboon³ 

[1] Department of Mathematics, Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin, RMUTR, Bangkok, Thailand;Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, KMUTT, Bangkok, Thailand

关键词: Hilbert Space;    Variational Inequality;    Iterative Algorithm;    Equilibrium Problem;    Nonexpansive Mapping;   

DOI  :  10.1155/2010/361512

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We introduce and analyze a new iterative algorithm for finding a common element of the set of fixed points of strict pseudocontractions, the set of common solutions of a system of generalized mixed equilibrium problems, and the set of common solutions of the variational inequalities with inverse-strongly monotone mappings in Hilbert spaces. Furthermore, we prove new strong convergence theorems for a new iterative algorithm under some mild conditions. Finally, we also apply our results for solving convex feasibility problems in Hilbert spaces. The results obtained in this paper improve and extend the corresponding results announced by Qin and Kang (2010) and the previously known results in this area.

【 授权许可】

CC BY