Some New Results for the J-Iterative Scheme in Kohlenbach Hyperbolic Space

Year 2022, Volume: 10 Issue: 2, 210 - 219, 31.10.2022

Aynur Şahin , Metin Basarır

Abstract

In the present paper, we study the J-iterative scheme of Bhutia and Tiwary (J. Linear Topol. Algebra, 8(4), (2019), 237-250) in Kohlenbach hyperbolic space. We prove the weak w^2-stability and data dependence theorems of this iterative scheme for contraction mappings. We also give some △-convergence and strong convergence theorems for generalized α-nonexpansive mappings and finite families of total asymptotically nonexpansive mappings using J-iterative scheme. The results presented here can be viewed as a generalization of several well-known results in CAT(0) space and uniformly convex Banach space.

Keywords

data dependence, fixed point, hyperbolic space, J-iterative scheme, strong convergence, weak w^2-stability, delta-convergence

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