Minimax theorems in fuzzy metric spaces

Journal Article · Tue May 15 04:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-017-0417-1· OSTI ID:22769334

Rashid, M. H. M., ^[1]

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1. Mu’tah University, Department of Mathematics and Statistics, Faculty of Science (Jordan)

A minimax theorem is a theorem providing conditions which guarantee that the max–min inequality is also an equality. The first theorem in this sense is von Neumann’s minimax theorem, which was considered the starting point of game theory. Since then, several alternative generalizations of von Neumann’s original theorem have appeared in the literature. Variational inequality and minimax problems are of fundamental importance in modern non-linear analysis. They are widely applied in mechanics, differential equations, control theory, mathematical economics, game theory, and optimization. The purpose of this paper is first to establish a minimax theorem for mixed lower–upper semi-continuous functions in fuzzy metric spaces which extends the minimax theorems of many von Neumann types. As applications, we utilize this result to study the existence problems of solutions for abstract variational inequalities and quasi-variational inequalities in fuzzy metric spaces and to study the coincidence problems and saddle problems in fuzzy metric spaces.

• OSTI ID: 22769334
• Journal Information: Computational and Applied Mathematics, Journal Name: Computational and Applied Mathematics Journal Issue: 2 Vol. 37; ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
CONTROL THEORY
DIFFERENTIAL EQUATIONS
FUZZY LOGIC
GAME THEORY
MATHEMATICAL SOLUTIONS
METRICS
OPTIMIZATION
PROBABILISTIC ESTIMATION
VARIATIONAL METHODS