A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi- ϕ -Asymptotically Nonexpansive Mapping in a Banach Space

Abstract

The purpose of this paper is to introduce the modified Halpern-type iterative method by the generalized f-projection operator for finding a common solution of fixed-point problem of a totally quasi-$\varphi$-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth andstrictly convex Banach space with the Kadec-Klee property. Consequently, we prove the strong convergence for a common solution of above two sets. Our result presented in this paper generalize and improvethe result of Chang et al., (2012), and some others.