The two main results of the paper are a theorem of the alternative of Gordan type and a two-function minimax theorem. Both are based on some weakened convexlike properties, without any vector space structure.
Anton Stefanescu. "A theorem of the alternative and a two-function minimax theorem." J. Appl. Math. 2004 (2) 169 - 177, 20 June 2004. https://doi.org/10.1155/S1110757X04304018