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Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems

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  • Rahul Shukla
  • Rekha Panicker

Abstract

This paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of α‐Krasnosel’skiĭ mapping associated with the newly defined class of mappings. Further, we present that α‐Krasnosel’skiĭ mapping associated with b‐enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning b‐enriched quasinonexpansive mappings have been proved.

Suggested Citation

  • Rahul Shukla & Rekha Panicker, 2023. "Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlaaa:v:2023:y:2023:i:1:n:5572893
    DOI: 10.1155/2023/5572893
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    References listed on IDEAS

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    1. Abbas, Mujahid & Anjum, Rizwan & Iqbal, Hira, 2022. "Generalized enriched cyclic contractions with application to generalized iterated function system," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
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