A new golden ratio iterative scheme for solving fixed point problems with application to image restoration problems
Abstract
The purpose of this paper is to introduce a new Golden Ratio Relaxed Three-Step Algorithm (GRRITA) for solving fixed point problems in Banach spaces. The proposed iterative scheme uses the golden ratio structure to enhance contraction effects, computational efficiency, and accelerate convergence. In addition, we establish strong convergence under weak assumptions, prove \(T\)-stability, data dependence, and error-estimation results, and demonstrate that GRRITA achieves Q-linear convergence with order one. Finally, we present some numerical experiments and an application to image restoration problems. The results validate our theoretical results, that is, the proposed iterative algorithm outperforms some existing iterative algorithms in the literature.
Copyright © 2026 Iyanu Sunday Mebawondu, Francis Akutsah, Ojen Kumar Narain, Adhir Maharaj. 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
I. S. Mebawondu, F. Akutsah, O. K. Narain, A. Maharaj, A new golden ratio iterative scheme for solving fixed point problems with application to image restoration problems, Adv. Fixed Point Theory 16 (2026), 38. https://doi.org/10.28919/afpt/10253
BibTeX
@article{Mebawondu2026,
author = {Mebawondu, Iyanu Sunday and Akutsah, Francis and Narain, Ojen Kumar and Maharaj, Adhir},
title = {A new golden ratio iterative scheme for solving fixed point problems with application to image restoration problems},
journal = {Adv. Fixed Point Theory},
volume = {16},
year = {2026},
pages = {38},
doi = {10.28919/afpt/10253}
}