Fixed Point Approximation of Generalized Nonexpansive Mappings in Hyperbolic Spaces

Abstract

We prove strong and Δ-convergence theorems for generalized nonexpansive mappings in uniformly convex hyperbolic spaces using S-iteration process due to Agarwal et al. As uniformly convex hyperbolic spaces contain Banach spaces as well as CAT(0) spaces, our results can be viewed as extension and generalization of several well-known results in Banach spaces as well as CAT(0) spaces.

Fixed point approximation of Picard normal S-iteration process for generalized nonexpansive mappings in hyperbolic spaces

“…The theorems presented in this paper generalizes corresponding theorems for uniformly convex normed spaces of Kadioglu and Yildirim [11] and CAT(0)-spaces of Abbas et al [1] and many others in this directions (see Itoh [8], Kim et al [14], Sahu [21] etc. ).…”

On fixed point convergence results for class of nonexpansivemappings in hyperbolic spaces via PJ iteration process

“…Many researchers attracted in the direction of approximating the fixed points of nonexpansive mapping and its generalized form [4,5,9,14,16,17,19,20,21,30] in a hyperbolic space.…”

On Some Strong and Δ- Convergence Results for SKC Mappings in Hyperbolic Spaces

“…x be a bounded sequence in a metric space X. We define a functional (.,{ }) : Many authors have studied the strong and △convergence of various iterative schemes in hyperbolic spaces (see [1], [6], [20], [21], [22], [23], [24]). In the next section, we establish strong and △convergence of S-iterative scheme in hyperbolic spaces for SKC mappings.…”