Minimax Theorems in Probabilistic Metric Spaces
نویسنده
چکیده
The minimax problem is of fundamental importance in nonlinear analysis and, especially, plays an important role in mathematical economics and game theory. The purpose of this paper is to obtain some minimax theorems for mixed lowerupper semi-continuous functions in probabilistic metric spaces which extend the minimax theorems of von Neumann types [1, 3, 4, 5, 6, 8, 10, 11, 12]. As applications, we utilise these results to study the existence problems of solutions for variational inequalities and implicit variational inequalities in probabilistic metric spaces and to show the existence of coincidence points and saddle points in probabilistic metric spaces. Throughout this paper, let R — (—oo,+oo) and R = [0,+oo). DEFINITION 1.1: A mapping F : R —> R is called a distribution function if it is nondecreasing and left-continuous with inf F(t) — 0 and sup F{t) = 1.
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