Hemi Equilibrium Problems on Hadamard Manifolds | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Volume 13, Issue 1, 2025, Pages 1-12 PDF (243.93 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2024.284685.1181 | ||
| Authors | ||
| Shreyasi Jana* 1; C. Nahak2 | ||
| 1Assistant Professor, Dept of Mathematics, Narajole Raj College, West Medinipur, West Bengal, India | ||
| 2Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India | ||
| Abstract | ||
| Throughout the years, equilibrium problems have been used to study various problems appearing in different fields of mechanics, physics, nonlinear programming, engineering mathematics, and so on (see for example, [7], [12]). Consequently, lots of research has been done on solving equilibrium problems under different circumstances in reflexive Banach spaces. This paper contemplates a generalized category of equilibrium problems on Hadamard manifolds called hemiequilibrium problems (HEP). We initiate the existence of solutions to hemiequilibrium problems (HEP) under the monotonicity assumption on the underlying bifunction by applying the KKM technique. We construct some counterexamples in the Hadamard manifold to rationalize our efforts. Additionally, we investigate a few iterative algorithms to solve hemiequilibrium problems on these nonlinear domains. Some particular instances of hemiequilibrium problems are demonstrated. These general classes of equilibrium problems are new on Hadamard manifolds. We hope our outcomes and ideas will spark further investigation in this fascinating and captivating field of research. | ||
| Keywords | ||
| Riemannian Geometry; Monotonicity; Fan-KKM Lemma | ||
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