Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via (p,q)-Calculus

Julalak Prabseang,Kamsing Nonlaopon,Sotiris K Ntouyas,Jessada Tariboon

doi:10.3390/math9040446

Abstract

In this paper, we present some new refinements of Hermite–Hadamard inequalities for continuous convex functions by using (p,q)-calculus. Moreover, we study some new (p,q)-Hermite–Hadamard inequalities for multiple integrals. Many results given in this paper provide extensions of others given in previous research.

Highlights

Mathematical inequalities play important roles in the study of mathematics as well as in other areas of mathematics because of their wide applications in mathematics and physics; see [1,2,3] for more details
Many researchers have been fascinated in the study of convex functions and, one of the well-known inequality for convex functions known as the Hermite–Hadamard inequality, which is defined as follows: f a+b 2
We aim to propose some new refinements of Hermite–Hadamard inequalities via (p, q)-calculus that have been expanded to integration on a finite interval of an n-dimensional

Summary

Introduction

Mathematical inequalities play important roles in the study of mathematics as well as in other areas of mathematics because of their wide applications in mathematics and physics; see [1,2,3] for more details. One of the most significant functions used to study many interesting inequalities is convex functions, which are defined as follows: Let I ⊂ R be a non-empty interval. The function f : I → R called as convex, if f (ta + (1 − t)b) ≤ t f (a) + (1 − t) f (b) holds for every a, b ∈ I and t ∈ [0, 1]. Many researchers have been fascinated in the study of convex functions and, one of the well-known inequality for convex functions known as the Hermite–Hadamard inequality, which is defined as follows: f a+b 2.

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Results

Conclusion