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Vietnam Journal of Mathematics 35:4(2007) 481-493

 Convex Conjugation and Duality for the Solutions of a Functional Equation

J.-E. Martínez-Legaz

Abstract.  We characterize the l.s.c. convex functions f: (0, +∞) -> that satisfy f(x) = xf(1/x) in terms of their Fenchel conjugates. We also introduce a suitable duality theory for such functions and characterize the associated support sets.

2000 Mathematics Subject Classification: 26A51.

Keywords: Convex functions, functional equations, Fenchel conjugates, generalized convex duality, abstract convexity.

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Published by Springer since January 2013