On conjugate trigonometrically ρ-convex functions

Abstract

The aim of this article is to introduce a definition of conjugate trigonometrically ρ-convex functions by using Young’s inequality which plays an important role in linking the concept of duality between trigonometrically ρ-convex functions, rather the definition given by Fenchel.  Furthermore, we show that the integration of any increasing function is trigonometrically ρ-convex.