The Viscosity Implicit Midpoint Rule for Finding Common Fixed Points of Two Asymptotically Nonexpansive Mappings with Applications

Shrijana Dhakal, Wutiphol Sintunavarat

Abstract

The purpose of this work is to introduce the viscosity implicit midpoint rule for finding the common fixed points of asymptotically nonexpansive mappings  in Hilbert spaces.  The strong convergence theorem of this method is proved under some favorable conditions imposed on the control parameters. Furthermore, it is shown that the limit solves an additional variational inequality problem. Also,  we include the applications to the variational inequality problems, constrained convex minimization problem, Fredholm integral equations and nonlinear evolution equation.