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Open AccessFeature PaperArticle

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

1
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani Sulaimani 46001, Kurdistan Region, Iraq
2
Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(4), 610; https://doi.org/10.3390/sym12040610
Received: 18 March 2020 / Revised: 25 March 2020 / Accepted: 25 March 2020 / Published: 12 April 2020
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. View Full-Text
Keywords: hermite–hadamard inequality; riemann–liouville fractional integrals; special functions hermite–hadamard inequality; riemann–liouville fractional integrals; special functions
MDPI and ACS Style

Mohammed, P.O.; Brevik, I. A New Version of the Hermite–Hadamard Inequality for Riemann–Liouville Fractional Integrals. Symmetry 2020, 12, 610.

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