APPROXIMATING FIXED POINTS FOR GENERALIZED α-NONEXPANSIVE MAPPING IN CAT(0) SPACE VIA NEW ITERATIVE ALGORITHM

Abstract

In this paper, we provide certain xed point results for a generalized α-nonexpansive mapping, as well as a new iterative algorithm called SRJ-iteration for approximating the fixed point of this class of mappings in the setting of CAT(0) spaces. Furthermore, we establish strong and Δ-convergence theorem for generalized α-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 results of Abbas et al. [10], Thakur et al. [22] and Piri et al. [19].