Some fixed points properties, strong and ∆-convergence results for generalized α-nonexpansive mappings in hyperbolic spaces

Abstract

In this paper, we introduce and study some fixed points properties and demiclosedness principle for generalized α-nonexpansive mappings in the frame work of uniformly convex hyperbolic spaces. We further establish strong and ∆-convergence theorems for Picard Normal S-iteration scheme generated by a generalized α-nonexpansive mapping in the frame work of uniformly convex hyperbolic spaces. The results obtained in this paper extend and generalize corresponding results in uniformly convex Banach spaces and many other results in this direction.