Annals of Functional Analysis

Refining and reversing the Fenchel inequality in convex analysis

Mustapha Raïssouli

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Our main goal in this article is to give some functional inequalities involving a (convex) functional and its Fenchel conjugate. As a consequence, we obtain some refinements of the so-called Fenchel inequality as well as its reverse. Inequalities of interest illustrating the previous theoretical results are provided as well.

Article information

Source
Ann. Funct. Anal., Volume 10, Number 2 (2019), 252-261.

Dates
Received: 16 June 2018
Accepted: 19 August 2018
First available in Project Euclid: 19 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.afa/1552960863

Digital Object Identifier
doi:10.1215/20088752-2018-0022

Mathematical Reviews number (MathSciNet)
MR3941386

Zentralblatt MATH identifier
07083893

Subjects
Primary: 46N10: Applications in optimization, convex analysis, mathematical programming, economics
Secondary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX] 39B72: Systems of functional equations and inequalities

Keywords
convex analysis Fenchel inequality refinement

Citation

Raïssouli, Mustapha. Refining and reversing the Fenchel inequality in convex analysis. Ann. Funct. Anal. 10 (2019), no. 2, 252--261. doi:10.1215/20088752-2018-0022. https://projecteuclid.org/euclid.afa/1552960863


Export citation

References

  • [1] J.-P. Aubin, L’analyse non linéaire et ses motivations économiques, Masson, Paris, 1986.
  • [2] I. Ekeland and R. Témam, Convex Analysis and Variational Problems, corrected reprint of the 1976 English original, Classics Appl. Math. 28, SIAM, Philadelphia, 1999.
  • [3] J.-P. Laurent, Approximation et optimisation, Enseign. Sci. 13, Hermann, Paris, 1972.
  • [4] M. Raïssouli and M. Chergui, Arithmetico-geometric and geometrico-harmonic means of two convex functionals, Sci. Math. Jpn. 55 (2002), no. 3, 485–492.
  • [5] E. Zeidler, Nonlinear Functional Analysis and Its Applications, III: Variational Methods and Optimization, Springer, New York, 1985.