Almost Convex Functions: Conjugacy and Duality

Radu Ioan Boţ (), Sorin-Mihai Grad () and Gert Wanka ()
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Radu Ioan Boţ: Chemnitz University of Technology
Sorin-Mihai Grad: Chemnitz University of Technology
Gert Wanka: Chemnitz University of Technology

A chapter in Generalized Convexity and Related Topics, 2007, pp 101-114 from Springer

Abstract: Summary We prove that the formulae of the conjugates of the precomposition with a linear operator, of the sum of finitely many functions and of the sum between a function and the precomposition of another one with a linear operator hold even when the convexity assumptions are replaced by almost convexity or nearly convexity. We also show that the duality statements due to Fenchel hold when the functions involved are taken only almost convex, respectively nearly convex.

Keywords: Fenchel duality; conjugate functions; almost convex functions; nearly convex functions (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-540-37007-9_5

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DOI: 10.1007/978-3-540-37007-9_5

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