Abstract
In this paper, we extends the classical theory of variational inequalities to the hyperbolic scalar setting using the structure of $\mathbb{D}$-Hilbert spaces. We introduce and analyze a new class of variational inequalities, termed general mildly $\mathbb{D}$-nonlinear variational inequalities, which generalize classical formulations by incorporating $\mathbb{D}$-nonlinear and product-type mappings. We characterize these problems in terms of their idempotent components and demonstrate that several known variational inequality problems, including Stampacchia-type and complementarity problems, emerge as special cases.
Key words: Hyperbolic numbers, product-type sets, product-type functions, $\mathbb{D}$-Lipschitz continuous, strongly $\mathbb{D}$-monotone, $\mathbb{D}$-Hilbert spaces.
Full Text
Article Information
| Title | A class of variational inequality in hyperbolic framework |
| Source | Methods Funct. Anal. Topology, Vol. 32 (2026), no. 1, 9-17 |
| DOI | 10.31392/MFAT-npu26_1.2026.02 |
| Milestones | Received 20/03/2025; Revised 20/09/2025 |
| Copyright | The Author(s) 2026 (CC BY-SA) |
Authors Information
Amjad Ali
Department of Mathematics, University of Jammu, Jammu 180001, INDIA
Romesh Kumar
Department of Mathematics, University of Jammu, Jammu 180001, INDIA
Citation Example
Amjad Ali and Romesh Kumar, A class of variational inequality in hyperbolic framework, Methods Funct. Anal. Topology 32
(2026), no. 1, 9-17.
BibTex
@article {MFAT2207,
AUTHOR = {Amjad Ali and Romesh Kumar},
TITLE = {A class of variational inequality in hyperbolic framework},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {32},
YEAR = {2026},
NUMBER = {1},
PAGES = {9-17},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_1.2026.02},
URL = {https://mfat.imath.kiev.ua/article/?id=2207},
}
