Abstract
In this work, we prove some strong and Δ convergence results for Reich-Suzuki type nonexpansive mappings through M iterative process. A uniformly convex hyperbolic metric space is used as underlying setting for our approach. We also provide an illustrate numerical example. Our results improve and extend some recently announced results of the metric fixed-point theory.
Highlights
E class of Suzuki type nonexpansive mappings was studied extensively by many authors
Pant and Pandey [22] used akur et al [10] iterative process to approximate fixed points of Reich–Suzuki type nonexpansive mappings. e purpose of this paper is to prove strong and Δ convergence results for Reich–Suzuki type nonexpansive mappings under M iterative process [12], which is known to converge faster Journal of Mathematics than the akur et al [10] iterative process
Kohlenbach [28] suggested the concept of generalized metric spaces and so-called hyperbolic metric spaces. is type of metric spaces includes normed spaces, the Hilbert ball with the hyperbolic metric, Cartesian products of Hilbert balls, metric trees, Hadamard manifolds, and CAT (0) spaces in the sense of Gromov. e definition is given as follows: A triplet (X, p, H) is called a hyperbolic metric space whenever (X, p) is a metric space and H: X × X × [0, 1] ⟶ X is a function such that for all a, b, w, s ∈ X and μ, ξ ∈ [0, 1], the following conditions hold
Summary
E class of Suzuki type nonexpansive mappings was studied extensively by many authors (cf. [10, 12,13,14,15,16,17,18,19,20,21]). Ullah and Arshad [12] proved some weak and strong convergence results of M iterative process for Suzuki type nonexpansive mappings in the context of Banach spaces. We study M iteration process for Reich–Suzuki type nonexpansive mappings in the setting of hyperbolic spaces.
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