A modified Mann iterative scheme for a sequence of‎ ‎nonexpansive mappings and a monotone mapping with applications

Abstract

‎In a real Hilbert space‎, ‎an iterative scheme is considered to‎ <br />‎obtain strong convergence which is an essential tool to find a‎ <br />‎common fixed point for a countable family of nonexpansive mappings‎ <br />‎and the solution of a variational inequality problem governed by a‎ <br />‎monotone mapping‎. ‎In this paper‎, ‎we give a procedure which results‎ <br />‎in developing Shehu's result to solve equilibrium problem‎. ‎Then‎, <br />‎we state more applications of this procedure‎. ‎Finally‎, ‎we‎ <br />‎investigate some numerical examples which hold in our main‎ <br />‎results‎.