On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces

In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and \Delta-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this paper extend and generalize corresponding results on uniformly convex Banach spaces, CAT(۰) spaces and many other results in this direction.

Keywords:

Banach operator , uniformly convex hyperbolic spaces , strong and Delta-convergence theorem , Modified Picard Normal S-iteration