Iterative Construction of Fixed Points for Operators Endowed with Condition (E) in Metric Spaces

Junaid Ahmad, Kifayat Ullah, Hüseyin Işik, Muhammad Arshad and Manuel de la Sen

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

Abstract: We consider the class of mappings endowed with the condition (E) in a nonlinear domain called 2‐uniformly convex hyperbolic space. We provide some strong and Δ‐convergence theorems for this class of mappings under the Agarwal iterative process. In order to support the main outcome, we procure an example of mappings endowed with the condition (E) and prove that its Agarwal iterative process is more effective than Mann and Ishikawa iterative processes. Simultaneously, our results hold in uniformly convex Banach, CAT(0), and some CAT(κ) spaces. This approach essentially provides a new setting for researchers who are working on the iterative procedures in fixed point theory and applications.

Date: 2021
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https://doi.org/10.1155/2021/7930128

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:7930128

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