Viscosity approximation of a common solution of fixed point, generalized equilibrium and constrained convex minimization problems
Abstract
In this paper, we introduce a viscosity iterative algorithm that approximates a common solution of constrained convex minimization problem, a generalized equilibrium problem involving averaged mapping and fixed point problem of 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 © 2025 Mengistu Goa Sangago, Timotewos Tone Dana, Wondimu Woldie Kassu. 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
M. G. Sangago, T. T. Dana, W. W. Kassu, Viscosity approximation of a common solution of fixed point, generalized equilibrium and constrained convex minimization problems, Adv. Fixed Point Theory 15 (2025), 19. https://doi.org/10.28919/afpt/9257
BibTeX
@article{Sangago2025,
author = {Sangago, Mengistu Goa and Dana, Timotewos Tone and Kassu, Wondimu Woldie},
title = {Viscosity approximation of a common solution of fixed point, generalized equilibrium and constrained convex minimization problems},
journal = {Adv. Fixed Point Theory},
volume = {15},
year = {2025},
pages = {19},
doi = {10.28919/afpt/9257}
}