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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. Mart\'inez-Legaz Abstract.  We characterize the l.s.c. convex functions $f:\left( 0,+\infty \right) \longrightarrow \overline{\R}$ that satisfy $f\left( x\right) =xf\left(1/x\right) $ 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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