Volume no :19, Issue no: 1, January 2013

AN INEQUALITY FOR LEGENDRE TRANSFORMATION

Author's: ALIREZA BEHTASH
Pages: [13] - [33]
Received Date: August 15, 2012; Revised November 13, 2012
Submitted by:

Abstract

Here, we prove a theorem for Legendre transformation of some specific derivative-like sequence chosen as the argument of Legendre transform of a function f using theory of convex functions, mean value theorem in one dimensional Euclidean space, and finally, a mathematical program established to provide some conditions of local convexity that may be incompatible with the existence of Legendre transformation. We also discuss the useful results of this theorem along with numerous examples. These results aim at providing a new set of Legendre transformations generated by a given convex function, where the variable of the function is regarded as an interval length. This generation is actually based on an appropriate modification of variables, which yields the treatment of Legendre transformations over a specific field of distributions.

Keywords

Legendre transformation, local convexity, quasiconvexity, pseudomean value.