A common minimum-norm solution of a generalized equilibrium problem and a fixed point problem for a countable family of nonexpansive mappings

Hathaikarn Wattanataweekul, Utith Inprasit, Weerayuth Nilsrakoo

Abstract

We introduce a new iterative scheme for finding a common

minimum-norm solution of a generalized equilibrium problem and a fixed point problem for a countable family of nonexpansive mappings and then establish strong convergence theorems of the scheme by using the NST-condition. Our result extends and improves the main result of Cai et al. \cite{CTL2012}, Chen \cite{C2012} and Yao et al. \cite{YZL2009} and

many others. Finally, we apply our results to solve the problem of finding common zeros of maximal monotone operators, the common minimizer problem, the multiple-sets split feasibility problem.