Strong convergence theorem for the modified generalized equilibrium problem and fixed point problem of strictly pseudo-contractive mappings

Fixexd point theory and applications

Sarawut Suwannaut¹  Atid Kangtunyakarn² 

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

关键词: strictly pseudo-contractive mapping;    K-mapping;    the modified generalized equilibrium problem;    equilibrium-like function;   

DOI  :  10.1186/1687-1812-2014-86

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this paper is to modify the generalized equilibrium problem introduced by Ceng et al. (J. Glob. Optim. 43:487-502, 2012) and to introduce the K-mapping generated by a finite family of strictly pseudo-contractive mappings and finite real numbers modifying the results of Kangtunyakarn and Suantai (Nonlinear Anal. 71:4448-4460, 2009). Then we prove the strong convergence theorem for finding a common element of the set of fixed points of a finite family of strictly pseudo-contractive mappings and a finite family of the set of solutions of the modified generalized equilibrium problem. Moreover, using our main result, we obtain the additional results related to the generalized equilibrium problem.

【 授权许可】

CC BY