THE VISCOSITY APPROXIMATION METHOD FOR THE IMPLICIT MIDPOINT RULE OF NONEXPANSIVE MAPPINGS IN BANACH SPACES

Abstract

The purpose of this paper is to introduce a viscosity approximation method for the implicit midpoint rule of nonexpansive mappings in Banach spaces. The strong convergence of this viscosity method is proved under certain assumptions imposed on the sequence of parameters. Applications to nonlinear variation inclusion problem and nonlinear Volterra integral equations are included. The results presented in the paper extend and improve some recent results announced in the current literature.