Approximating fixed points of α-convex generalized nonexpansive mappings

Rahul Shukla, Rekha Panicker, Deepa Vijayasenan

Abstract


The objective of our paper is to introduce a novel category of nonlinear mappings namely α-convex generalized nonexpansive and demonstrate different existence and convergence theorems for this type of mappings in Banach spaces under various assumptions. We show that this class of mappings admits an approximate fixed point sequence in each nonempty bounded closed convex Φ-invariant subset of Banach spaces. Moreover, we provide an example to support the results presented in our study. Furthermore, we expand upon the findings reported by T. Suzuki (J. Math. Anal. Appl., 340(2): 1088–1095, 2008).

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Published: 2024-03-25

How to Cite this Article:

Rahul Shukla, Rekha Panicker, Deepa Vijayasenan, Approximating fixed points of α-convex generalized nonexpansive mappings, Adv. Fixed Point Theory, 14 (2024), Article ID 9

Copyright © 2024 Rahul Shukla, Rekha Panicker, Deepa Vijayasenan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

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