Convergence theorem of κ -strictly pseudo-contractive mapping and a modifıcation of generalized equilibrium problems

Fixexd point theory and applications

Atid Kangtunyakarn¹ 

[1] Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok, Thailand

关键词: nonexpansive mappinga;    strictly pseudo-contractive mapping;    generalized equilibrium problem;    inverse-strongly monotone;    variational inequality problem;   

DOI  :  10.1186/1687-1812-2012-89

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this article, we first introduce strong convergence theorem of κ-strictly pseudo-contractive mapping without assumption of the mapping S = κI + (1 - κ)T. Then, we prove strong convergence of proposed iterative scheme for finding a common element of the set of fixed points of κ-strictly pseudo-contractive mapping and the set of solution of a modification of generalized equilibrium problem. Moreover, by using our main result and a new lemma in the last section we obtain strong convergence theorem for finding a common element of the set of fixed points of κ-strictly pseudo-contractive mapping and two sets of solutions of variational inequalities.

【 授权许可】

CC BY