Strongly convergent doubly accelerated forward-backward algorithm for monotone inclusion and fixed point problems
Abstract
In this paper, we study the development of efficient iterative algorithm for finding a common solution to monotone inclusion problems and fixed point problems in real Hilbert spaces. These problems arise naturally in optimization, equilibrium modeling, signal processing, and other applied fields. We propose a doubly accelerated forward-backward algorithm with a viscosity term, combining inertial techniques and extragradient steps to enhance convergence speed and stability. The proposed algorithm relaxes restrictive assumptions on the underlying operators and guarantees strong convergence under mild conditions. Extensive numerical experiments illustrate the effectiveness and superiority of our method compared to existing approaches.
Copyright © 2026 Austine Efut Ofem, Seithuti Philemon Moshokoa, Malesela Clifford Kekana. 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
A. E. Ofem, S. P. Moshokoa, M. C. Kekana, Strongly convergent doubly accelerated forward-backward algorithm for monotone inclusion and fixed point problems, Adv. Fixed Point Theory 16 (2026), 24. https://doi.org/10.28919/afpt/9887
BibTeX
@article{Ofem2026,
author = {Ofem, Austine Efut and Moshokoa, Seithuti Philemon and Kekana, Malesela Clifford},
title = {Strongly convergent doubly accelerated forward-backward algorithm for monotone inclusion and fixed point problems},
journal = {Adv. Fixed Point Theory},
volume = {16},
year = {2026},
pages = {24},
doi = {10.28919/afpt/9887}
}