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On stability analysis for generalized Minty variational-hemivariational inequality in reflexive Banach spaces
Lu-Chuan Ceng1, Ravi P Agarwal2,3, Jen-Chih Yao4
11Department of Mathematics, Shanghai Normal University, Shanghai, China.
Journal of Inequalities and Applications
|March 7, 2019
Summary
This study explores the stability of generalized Minty variational-hemivariational inequalities in Banach spaces. We establish equivalent characterizations and present a key stability result for -pseudomonotone mappings.
Area of Science:
- Mathematical Analysis
- Optimization Theory
Background:
- Variational-hemivariational inequalities are crucial in modeling complex systems.
- Understanding their stability is essential for practical applications.
Purpose of the Study:
- To analyze the stability of generalized Minty variational-hemivariational inequalities.
- To provide equivalent characterizations of these inequalities.
- To establish a stability result for a specific class of mappings.
Main Methods:
- Utilizing concepts from functional analysis in reflexive Banach spaces.
- Developing equivalent formulations of the inequalities.
- Applying fixed-point theorems and monotonicity concepts.
Main Results:
- Equivalent characterizations for generalized Minty variational-hemivariational inequalities are demonstrated.
- A significant stability result is proven for inequalities involving -pseudomonotone mappings.
Conclusions:
- The findings contribute to the theoretical understanding of variational-hemivariational inequalities.
- The established stability result enhances the analysis of related mathematical models.
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