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Vietnam Journal of Mathematics 35:4(2007)
481-493
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Convex Conjugation and Duality for the
Solutions of a Functional Equation
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J.-E.
Martínez-Legaz
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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.
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2000 Mathematics Subject Classification: 26A51.
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Keywords: Convex functions, functional equations,
Fenchel conjugates, generalized convex duality, abstract convexity.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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