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Journal of Convex Analysis 09 (2002), No. 1, 259--268
Copyright Heldermann Verlag 2002

Coincidence Theorems for Convex Functions

Joël Benoist
Faculté des Sciences, Université de Limoges, 123 Av. Albert Thomas, 87060 Limoges, France

Aris Daniilidis
Lab. de Mathématiques Appliquées, Université de Pau et des Pays de l'Adour, 64000 Pau, France

The paper aims at creating a new insight into our perception of convexity by focusing on two fundamental problems: the coincidence of two functions (at least one being convex) upon an information on a dense set and the clarification of the relation between convexity and Fenchel subdifferential. Various results are established into these directions. Several examples are also illustrated showing that some rather unexpected situations can often occur.

Keywords: Convex function, coincidence, subdifferential.

MSC: 52A41, 49J52; 26E99

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