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Journal of Convex Analysis 10 (2003), No. 1, 229--244
Copyright Heldermann Verlag 2003

Functional Logarithm in the Sense of Convex Analysis

Mustapha Raïssouli
Groupe AFA - UFR AFACS, Université Moulay Ismaïl, Faculté des Sciences, Dép. de Mathématiques et Informatique, BP 4010, Zitoune, Meknés, Marocco, raissoul@fsmek.ac.ma

Hanane Bouziane
Groupe AFA - UFR AFACS, Université Moulay Ismaïl, Faculté des Sciences, Dép. de Mathématiques et Informatique, BP 4010, Zitoune, Meknés, Marocco

We introduce a map, operating on the cone of lower semicontinuous convex functionals, which extends the Logarithm from positive invertible operators to convex functionals. Afterwards, we present a second order functional limited development extending that of operators. The paper will be illustrated with some examples which justify the chosen terminology and the importance of this work.

Keywords: Convex analysis, conjugate function, subdifferential, functional logarithm, functional limited development.

MSC 2000: 49-XX, 52-XX.

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