Abstract

This paper deals with the SRJ iteration process for approximating the fixed point of generalized $(\alpha,\beta)-$nonexpansive mappings in hyperbolic spaces. Furthermore, we establish a strong and $\Delta$-converges theorem for generalized $(\alpha, \beta)$-nonexpansive mapping in hyperbolic space. Finally, we present a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature. Our results obtained in this paper improve, extend and unify some related results in the literature.

Keywords and Phrases

Hyperbolic spaces, generalized $(\alpha,\beta)-$nonexpansive mapping, strong and $\Delta$-convergence theorems.

A.M.S. subject classification

47H10, 54H25, 54E50.

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