Ding, Xie Ping; Tan, Kok-Keong A minimax inequality with applications to existence of equilibrium point and fixed point theorems. (English) Zbl 0833.49009 Colloq. Math. 63, No. 2, 233-247 (1992). Ky Fan’s minimax inequality has become a versatile tool in nonlinear and convex analysis. In this paper, we obtain a minimax inequality which generalizes those generalizations of Ky Fan’s minimax inequality due to G. Allen, C. L. Yen, K. K. Tan, J. S. Bae, W. K. Kim and K. K. Tan and Fan himself. Several equivalent forms are then formulated and one of them, the maximal element version, is used to obtain a fixed point theorem which in turn is applied to obtain an existence theorem of an equilibrium point in a one-person game. Next, by applying the minimax inequality, we present some fixed point theorems for set-valued inward and outward mappings on a non-compact convex set in a topological vector space. Cited in 1 ReviewCited in 70 Documents MSC: 49J35 Existence of solutions for minimax problems 47H10 Fixed-point theorems 47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics Keywords:Ky Fan’s minimax inequality; maximal element version; equilibrium point; one-person game; fixed point theorems; set-valued inward and outward mappings PDFBibTeX XMLCite \textit{X. P. Ding} and \textit{K.-K. Tan}, Colloq. Math. 63, No. 2, 233--247 (1992; Zbl 0833.49009) Full Text: DOI EuDML