Auxiliary principle technique for general harmonic variational inequalities
Abstract
In this Paper, we have introduced and analyzed certain new types of harmonic variational inequalities, such as Auxiliary general Harmonic variational inequalities. The optimality conditions of general harmonic convex functions are shown to be specified by auxiliary general harmonic variational inequalities. Using the harmonic variational inequality, it is demonstrated that the harmonic convex set’s minimum of a differentiable harmonic convex function may be described. In addition to the auxiliary principle technique, other hybrid proximal point methods are proposed. The convergence of the proposed method is shown to depend only on the operator being pseudo-monotonic, which is a weaker criterion than monotonicity. The findings presented in this work may encourage more study in this area.
Copyright © 2025 Netra Kumar Gupta, Suja Varghese, M.A. Siddiqui. 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
N. K. Gupta, S. Varghese, M. A. Siddiqui, Auxiliary principle technique for general harmonic variational inequalities, Adv. Fixed Point Theory 15 (2025), 26. https://doi.org/10.28919/afpt/9227
BibTeX
@article{Gupta2025,
author = {Gupta, Netra Kumar and Varghese, Suja and Siddiqui, M.A.},
title = {Auxiliary principle technique for general harmonic variational inequalities},
journal = {Adv. Fixed Point Theory},
volume = {15},
year = {2025},
pages = {26},
doi = {10.28919/afpt/9227}
}