A new iterative algorithm for generalized (α,β)-nonexpansive mapping in CAT(0) space

Abstract

In this paper, we provide certain fixed point results for a generalized (α,β)-nonexpansive mapping, as well as a new iterative algorithm for approximating the fixed point of this class of mappings in the setting of CAT(0) spaces. Furthermore, we establish strong and ∆-converges theorem for generalized (α,β)-nonexpansive mapping in CAT(0) 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.