A theorem of the alternative and a two-function minimax theorem. (English) Zbl 1095.49022

Stefanescu, Anton

J. Appl. Math. 2004, No. 2, 169-177 (2004).

Based on his definitions of weakly convexlike and affine weakly convexlike families of functions, the author presents an abstract alternative theorem and a minimax inequality theorem. These theorems extend previous results and do not require vector or topological structures.

Reviewer: Dumitru Motreanu (Perpignan)

MSC:

49K35	Optimality conditions for minimax problems
90C47	Minimax problems in mathematical programming
26B25	Convexity of real functions of several variables, generalizations

Keywords:

minimax inequality; alternative; convexlike family of functions; weakly convexlike family of functions