A maximum theorem for generalized convex functions
DOI:
https://doi.org/10.24193/subbmath.2022.1.02Keywords:
Maximum theorem, generalized convex function.Abstract
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.
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