fgh-Convex Functions and Entropy Bounds

Abstract

In this paper, we introduce an universal definition (fgh-convex) that results in several types of convexity. Particular cases of the fgh-convex are for instance the harmonically convex, geometrically convex, GA-convex, log-convex, and several others. Also, we obtain some useful inequalities such as Jensen, generalization of Jensen Hermite-Hadamard, Mercer inequalities. Moreover, with the use of these inequalities, we obtained bounds for Shannon’s entropy and Kapur’s entropy. Finally, we found an application of the obtained inequalities in means.

KEYWORDS:

• fgh-convex function
• Jensens inequality
• Kapur’s entropy
• Shannon’s entropy

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 26B25
• 26D20

Disclosure statement

The authors declare that they have no competing interests.