In this paper a notion of difference function f is introduced for real-valued, non-negative and log-concave functions f defined in the n dimensional Euclidean space. The difference function represents a functional analog of the difference body K + (−K) of a convex body K. The main result is a sharp inequality which bounds the integral of f from above in terms of the integral of f. Equality conditions are characterized.
Functional inequalities related to the Rogers-Shephard inequality / A. COLESANTI. - In: MATHEMATIKA. - ISSN 0025-5793. - STAMPA. - 53:(2006), pp. 81-101.
Functional inequalities related to the Rogers-Shephard inequality
COLESANTI, ANDREA
2006
Abstract
In this paper a notion of difference function f is introduced for real-valued, non-negative and log-concave functions f defined in the n dimensional Euclidean space. The difference function represents a functional analog of the difference body K + (−K) of a convex body K. The main result is a sharp inequality which bounds the integral of f from above in terms of the integral of f. Equality conditions are characterized.
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