A New Strong Convergence Theorem for Equilibrium Problems and Fixed Point Problems in Banach Spaces

Fixexd point theory and applications

Weerayuth Nilsrakoo¹ 

[1] Department of Mathematics, Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani, Thailand

关键词: Hilbert Space;    Banach Space;    Equilibrium Problem;    Nonexpansive Mapping;    Strong Convergence;   

DOI  :  10.1155/2011/572156

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We introduce a new iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach space. Then, we study the strong convergence of the sequences. With an appropriate setting, we obtain the corresponding results due to Takahashi-Takahashi and Takahashi-Zembayashi. Some of our results are established with weaker assumptions.

【 授权许可】

CC BY