A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space

Abstract

Abstract In this paper, the common solution problem (P1) of generalized equilibrium problems for a system of inverse-strongly monotone mappings and a system of bifunctions satisfying certain conditions, and the common fixed-point problem (P2) for a family of uniformly quasi-ϕ-asymptotically nonexpansive and locally uniformly Lipschitz continuous or uniformly Hölder continuous mappings are proposed. A new iterative sequence is constructed by using the generalized projection and hybrid method, and a strong convergence theorem is proved on approximating a common solution of (P1) and (P2) in Banach space. 2000 MSC: 26B25, 40A05

Keywords

• Common solution
• Equilibrium problem
• Fixed-point problem
• Iterative sequence
• Strong convergence