Bot, Radu Ioan ; Grad, Sorin Mihai ; Wanka, Gert : Almost Convex Functions: Conjugacy and Duality

Author(s):

Bot, Radu Ioan
Grad, Sorin Mihai
Wanka, Gert

Title:

Almost Convex Functions: Conjugacy and Duality

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 15, 2005

Mathematics Subject Classification:

42A50			[ Conjugate functions, conjugate series, singular integrals ]
26A51			[ Convexity, generalizations ]
49N15			[ Duality theory ]

Abstract:

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

Language:

English

Publication time:

9 / 2005