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

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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