A New Version of the Hermite–Hadamard Inequality for Riemann–Liouville Fractional Integrals

Abstract

Integral inequalities play a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods. Thus, the present days need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. The concept of convexity plays a strong role in the field of inequalities due to the behavior of its definition. There is a strong relationship between convexity and symmetry. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the past few years. In this article, we firstly point out the known Hermite–Hadamard (HH) type inequalities which are related to our main findings. In view of these, we obtain a new inequality of Hermite–Hadamard type for Riemann–Liouville fractional integrals. In addition, we establish a few inequalities of Hermite–Hadamard type for the Riemann integrals and Riemann–Liouville fractional integrals. Finally, three examples are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function.