A common solution of constrained convex minimization problem, generalized equilibrium problem and fixed point problem of directed nonexpansive mappings
Abstract
In this paper, we introduce an iterative algorithm that approximates a common solution of a constrained minimization problem of convex function, a generalized equilibrium problem involving averaged mapping, and fixed point problem of a directed nonexpansive mapping. We prove the strong convergence of the proposed iterative algorithm to a common solution that satisfies a variational inequality under some suitable conditions on the parameters. It generalizes the familiar gradient-projection algorithm for convex minimization problem. This result improves and extends some recent results in the literature.
Copyright © 2026 Orebonye Ramatebele, Mengistu Goa Sangago, Abebe Regassa Tufa. 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
O. Ramatebele, M. G. Sangago, A. R. Tufa, A common solution of constrained convex minimization problem, generalized equilibrium problem and fixed point problem of directed nonexpansive mappings, Adv. Fixed Point Theory 16 (2026), 8. https://doi.org/10.28919/afpt/9703
BibTeX
@article{Ramatebele2026,
author = {Ramatebele, Orebonye and Sangago, Mengistu Goa and Tufa, Abebe Regassa},
title = {A common solution of constrained convex minimization problem, generalized equilibrium problem and fixed point problem of directed nonexpansive mappings},
journal = {Adv. Fixed Point Theory},
volume = {16},
year = {2026},
pages = {8},
doi = {10.28919/afpt/9703}
}