Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Convex analysis
  • conjugate function
  • subdifferential
  • functional logarithm
  • functional limited development

Mathematics Subject Classification

49-XX, 52-XX

Suggested citation

M. Raissouli, H. Bouziane. “Functional Logarithm in the Sense of Convex Analysis.” Journal of Convex Analysis 10 (2003), No. 1, 229–244.

Copyright Heldermann Verlag 2003