Modified Iterative Scheme for Multivalued Nonexpansive Mappings, Equilibrium Problems and Fixed Point Problems in Banach Spaces

Abstract

In this research, we modified iterative scheme for finding common element of the set of fixed point of total quasi-\(\phi \)-asymptotically nonexpansive multivalued mappings, the set of solution of an equilibrium problem and the set of fixed point of relatively nonexpansive mappings in Banach spaces. In addition, the strong convergence for approximating common solution of our mentioned problems is proved under some mild conditions. Our results extend and improve some recent results announced by some authors. We divide our research details into three main sections including Introduction, Preliminaries, Main Results. First, we introduce the backgrounds and motivations of this research and follow with the second section, Preliminaries, which mention about the tools that will be needed to prove our main results. In the last section, Main Results, we propose the theorem and corollary which is the most important part in our research.