Annals of Functional Analysis

Refining and reversing the Fenchel inequality in convex analysis

Mustapha Raïssouli

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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

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

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

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Zentralblatt MATH identifier

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

convex analysis Fenchel inequality refinement


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.

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