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

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-&#981;-asymptotically nonexpansive and locally uniformly Lipschitz continuous or uniformly H&#246;lder 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</p