Hermite-Hadamard type Inequalities via $p$--Harmonic Exponential type Convexity and Applications

Abstract

In this work, we introduce the idea and concept of $p$--harmonic exponential type convex functions. We elaborate on the newly introduced idea by examples and some interesting algebraic properties. In addition, we attain the novel version of Hermite--Hadamard type inequality in the mode of the newly introduced definition and on the basis of lemmas, some refinements of the Hermite--Hadamard type inequalities in the support of the newly introduced idea are established. Finally, we investigate and explore some integral inequalities in the form of applications for the arithmetic, geometric, harmonic and logarithmic means. The amazing tools and interesting ideas of this work may inspire and motivate further research in this direction furthermore.

Keywords

• hermite--hadamard type inequality
• , harmonic convex functions
• , p-harmonic exponential type convex functions