Existence and approximation of a fixed point of a fundamentally nonexpansive mapping in hyperbolic spaces

Abstract

We prove that a fundamentally nonexpansive mapping on a compact and convex subset of a hyperbolic space, has a fixed point. We also show that one-step iterative algorithm of two mappings is vital for the approximation of a common fixed point of two fundamentally nonexpansive mappings in a strictly convex hyperbolic space. Our results are new in metric fixed point theory and generalize several existing results.