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

* Correspondence: czcheng@bjut. edu.cn College of Applied Science, Beijing University of Technology, Beijing 100124, PR China Full list of author information is available at the end of the article Abstract In this paper, the common solution problem (P1) of generalized equilibrium problems for a system of inverse-strongly monotone mappings {Ak}k=1 and a system of bifunctions {fk}k=1 satisfying certain conditions, and the common fixed-point problem (P2) for a family of uniformly quasi-j-asymptotically nonexpansive and locally uniformly Lipschitz continuous or uniformly Hölder continuous mappings {Si}i=1 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