A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space
De-ning Qu, Cao-zong Cheng · Fixed Point Theory and Applications · 2011
Abstract In this paper, the common solution problem (P1) of generalized equilibrium problems for a system of inverse-strongly monotone mappings "Equation missing" and a system of bifunctions "Equation missing" 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 "Equation missing" 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