The viscosity method for the implicit double midpoint rule with numerical results and its applications

Abstract

In this work, we present the viscosity method for the implicit double midpoint rule for finding the fixed points of nonexpansive mappings in real Hilbert spaces. The strong convergence theorem of this method is proved under some specific assumption imposed on the control parameters. Also, we present some numerical results which are presented to illustrate the proposed method and convergence results. Moreover, we provide the applications to the variational inequality problems, constrained convex minimization problems, nonlinear evolution equations, and Fredholm integral equations.