Fixed Point Approximation of Nonexpansive Mappings on a Nonlinear Domain

Abstract

We use a three-step iterative process to prove some strong and $\mathrm{\Delta }$-convergence results for nonexpansive mappings in a uniformly convex hyperbolic space, a nonlinear domain. Three-step iterative processes have numerous applications and hyperbolic spaces contain Banach spaces (linear domains) as well as CAT(0) spaces. Thus our results can be viewed as extension and generalization of several known results in uniformly convex Banach spaces as well as CAT(0) spaces.