Abstract
In this paper, we introduce the class of $SKC$ -mappings, which is a generalization of the class of Suzuki-generalized nonexpansive mappings, and we prove the strong and Δ-convergence theorems of the S-iteration process which is generated by $SKC$ -mappings (Karapinar and Tas in Comput. Math. Appl. 61:3370-3380, 2011) in uniformly convex hyperbolic spaces. As uniformly convex hyperbolic spaces contain Banach spaces as well as $\operatorname {CAT}(0)$ spaces, our results can be viewed as an extension and generalization of several well-known results in Banach spaces as well as $\operatorname {CAT}(0)$ spaces.
Highlights
We give some definitions for the main results.Definition
In [ ], Suzuki proved the existence of the fixed point and convergence theorems for mappings satisfying condition (C) in Banach spaces
The purpose of this paper is to prove some strong and -convergence theorems of the S-iteration process which is generated by SKC-mappings in uniformly convex hyperbolic spaces
Summary
We give some definitions for the main results.Definition. Let C be a nonempty subset of a Banach space X. In [ ], Suzuki proved the existence of the fixed point and convergence theorems for mappings satisfying condition (C) in Banach spaces.
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