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Authors: ZSOLT PÁLES.
DOI: 10.24193/subbmath.2022.1.02
Published Online: 2022-03-10
Published Print: 2022-03-31
pp. 21-29
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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.
Keywords: Maximum theorem, generalized convex function.
Mathematics Subject Classification (2010): 39B22, 39B52.
