Viscosity Approximation Methods for Zeros of Accretive Operators and Fixed Point Problems in Banach Spaces

Abstract

In this paper, we introduce iterative algorithms for finding a zero of set-valued accretive operators by the viscosity approximation method based on Meir–Keeler-type contractions in a reflexive Banach space which admits a weakly continuous duality mapping. We obtain some strong convergence theorems under suitable conditions. As applications, we apply our results for finding common fixed point of nonexpansive semigroups and for solving equilibrium problem, optimization problem, and variational inequalities.