A common solution of variational inclusion problem involving maximal η-relaxed monotone mapping and fixed point problem of nonlinear mapping on Banach spaces
Abstract
Let \(E\) be a real uniformly convex and uniformly smooth Banach space with the dual space \(E^*\). Let \(J:E\to E^*\) be the normalized duality mapping and \(A:E\to 2^{E^*}\) a maximal \(\eta\)-relaxed monotone mapping. The purpose of this article is two fold. First we present the characterizations of \(\eta\)-relaxed monotone mappings on uniformly convex and uniformly smooth Banach spaces, and also some properties of the resolvent mapping associated with maximal \(\eta\)-relaxed monotone mapping are proved. Secondly, iterative algorithms for approximating a common element of the set of fixed points of nonlinear mapping and the set of solution of variational inclusion problems involving maximal \(\eta\)-relaxed mappings is proposed, and then strong convergence theorems are proved. The results improve and extend some recent results in the literature.
Copyright © 2025 Mengistu Goa Sangago, Hiwot Redda Gebre. 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, H. R. Gebre, A common solution of variational inclusion problem involving maximal η-relaxed monotone mapping and fixed point problem of nonlinear mapping on Banach spaces, Adv. Fixed Point Theory 15 (2025), 54. https://doi.org/10.28919/afpt/9655
BibTeX
@article{Sangago2025,
author = {Sangago, Mengistu Goa and Gebre, Hiwot Redda},
title = {A common solution of variational inclusion problem involving maximal η-relaxed monotone mapping and fixed point problem of nonlinear mapping on Banach spaces},
journal = {Adv. Fixed Point Theory},
volume = {15},
year = {2025},
pages = {54},
doi = {10.28919/afpt/9655}
}