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Some fixed point theorems for generalized enriched nonexpansive mappings in Banach spaces

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Abstract

In this paper, we introduce a new class of mappings, namely, generalized enriched nonexpansive mappings. Some examples are presented to ensure the existence of this class of mappings. We prove a number of weak and strong convergence theorems for Kirk iterative method in the setting of Banach spaces. These results are generalizations of the results in Berinde (Carpathian J Math 35(3):293–304, 2019) and Berinde (Carpathian J Math 36(1):27–34, 2020).

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Acknowledgements

The authors thank the reviewers for their important comments and valuable suggestions which were useful to improve this paper.

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  1. Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha, 5117, South Africa

    Rahul Shukla & Rekha Panicker

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  1. Rahul Shukla
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  2. Rekha Panicker
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Correspondence to Rekha Panicker.

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Shukla, R., Panicker, R. Some fixed point theorems for generalized enriched nonexpansive mappings in Banach spaces. Rend. Circ. Mat. Palermo, II. Ser 72, 1087–1101 (2023). https://doi.org/10.1007/s12215-021-00709-4

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  • DOI: https://doi.org/10.1007/s12215-021-00709-4

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