Approximating fixed points of α-convex generalized nonexpansive mappings
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).
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.
Cite this article
R. Shukla, R. Panicker, D. Vijayasenan, Approximating fixed points of α-convex generalized nonexpansive mappings, Adv. Fixed Point Theory 14 (2024), 9. https://doi.org/10.28919/afpt/8421
BibTeX
@article{Shukla2024,
author = {Shukla, Rahul and Panicker, Rekha and Vijayasenan, Deepa},
title = {Approximating fixed points of α-convex generalized nonexpansive mappings},
journal = {Adv. Fixed Point Theory},
volume = {14},
year = {2024},
pages = {9},
doi = {10.28919/afpt/8421}
}