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Generalised Nonlinear Variational Inequality Problems with Random Variation
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Version 1
: Received: 6 August 2024 / Approved: 6 August 2024 / Online: 8 August 2024 (12:00:18 CEST)
How to cite: Gissy, H.; Salahuddin, .. Generalised Nonlinear Variational Inequality Problems with Random Variation. Preprints 2024, 2024080454. https://doi.org/10.20944/preprints202408.0454.v1 Gissy, H.; Salahuddin, .. Generalised Nonlinear Variational Inequality Problems with Random Variation. Preprints 2024, 2024080454. https://doi.org/10.20944/preprints202408.0454.v1
Abstract
This text deals with exploring random solutions for generalized nonlinear variational inequality problems. Using the Fan-KKM theorem and Aumann's measurable selection theorem, we are able to prove the existence and uniqueness of random solution sets under the conditions of monotonicity and convexity. Additionally, we use Minty's lemma to demonstrate the compactness and convexity of the random solution sets.
Keywords
generalized nonlinear random variational inequality problems; measurable spaces; Gwinner’s section theorem; Aummann’s measurable selection; Minty,s lemma; solution sets
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: 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.
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