A maximum theorem for generalized convex functions - PÁLES, Zsolt (Studia Universitatis Babeș-Bolyai Mathematica, 2022)
Motivated by the Maximum Theorem for convex functions (in the setting of linear spaces) and for subadditive functions (in the setting of Abelian semigroups), we establish a Maximum Theorem for the class of generalized convex functions, i.e., for functions $f:X o X$ that satisfy the inequality $f(xcirc y)leq pf(x)+qf(y)$, where $circ$ is a binary operation on $X$ and $p,q$ are positive constants. As an application, we also obtain an extension of the Karush--Kuhn--Tucker theorem for this class of functions. Mathematics Subject Classification (2010): 39B22, 39B52. Received 19 December 2021; Accepted 29 December 2021.