Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space

Journal of inequalities and applications

Mohammad Farid¹ 

关键词: generalized equilibrium problem;    variational inequality problem;    fixed point problem;    relatively nonexpansive mappings;    iterative scheme;   

DOI  :  10.1186/s13660-017-1574-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space. Further, we prove the strong convergence of the sequences generated by the iterative scheme. Finally, we derive some consequences from our main result. Our work is an improvement and extension of some previously known results recently obtained by many authors.

【 授权许可】

CC BY