Full characterizations of minimax inequality, fixed point theorem, saddle point theorem, and KKM principle in arbitrary topological spaces

A Discrete Characterization of the Solvability of Equilibrium Problems and Its Application to Game Theory

“…The convexity conditions considered in the above corollary are different from the concept of α-transfer quasiconvexity considered in [13,28]: if X is a nonempty and convex subset of a linear space and Y is a nonempty set, f : X × Y → R is α-transfer quasiconvex on Y if given m ≥ 1 and y 1 , . .…”

A minimax approach for inverse variational inequalities

“…We make use of the following classical minimax theorem ( [8,14,23]). More general or different versions can be found, for instance, in [25,26,27,33,32,35,36]. This result has been used, in an equivalent form of theorem of the alternative, or that of Hahn-Banach type result, to characterize the existence of a solution for nonlinear infinite programs: see [20,21,22,28].…”