A Hybrid Subgradient Algorithm for Finding a Common Solution of Pseudomonotone Equilibrium Problems and Hierarchical Fixed Point Problems of Nonexpansive Mappings

Rattanaporn Wangkeeree, Kiattisak Rattanaseeha, Rabian Wangkeeree

Abstract

We propose a new strongly convergent algorithm for finding a common point in the solution set of a class of pseudomonotone equilibrium problems and the set of fixed points of a nonexpansive mappings in a real Hilbert space. The strong convergence theorem of proposed algorithms is investi- gated without the Lipschitz condition for the bifunctions. Our results complement many known recent results in the literature.