Giaccardi inequality for generalized convex functions and related results

Abstract

Abstract In this article, the famous Giaccardi inequality is generalized for modified ( h , m ) $(h,m)$ -convex functions under the condition that h is a multiplicative positive function. The results are also discussed for different values of h and m. Also, Lagrange and Cauchy type mean value theorems for the functional due to Giaccardi’s inequality are obtained.

Keywords

• Modified h-convex functions
• Modified ( h , m ) $(h,m)$ -convex functions
• Giaccardi inequality