A maximum theorem for generalized convex functions
A maximum theorem for generalized convex functions
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 $f:X\to\R$ that satisfy the inequality $f(x\circ y)\leq pf(x)+qf(y)$, where $\circ$ is …