Strong convergence of iterative algorithms with variable coefficients for generalized equilibrium problems, variational inequality problems and fixed point problems

Fixexd point theory and applications

Lin Zhao¹  Ci-Shui Ge¹  Neng-Fu Yu² 

[1] Department of Mathematics and Physics, Anhui University of Architecture, Hefei, Anhui, People’s Republic of China

关键词: generalized equilibrium problem;    variational inequality;    fixed point;    asymptotically strict pseudocontractive mapping in the intermediate sense;    algorithm with variable coefficients;   

DOI  :  10.1186/1687-1812-2013-257

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we propose some new iterative algorithms with variable coefficients for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping and the set of common fixed points of a finite family of asymptotically κ-strict pseudocontractive mappings in the intermediate sense. Some strong convergence theorems of these iterative algorithms are obtained without some boundedness conditions which are not easy to examine in advance. The results of the paper improve and extend some recent ones announced by many others. The algorithms with variable coefficients introduced in this paper are of independent interests. MSC:47H09, 47H10, 47J20.

【 授权许可】

CC BY