Some ( p, q )-Integral Inequalities of Hermite–Hadamard Inequalities for ( p, q )-Differentiable Convex Functions

Waewta Luangboon, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas and Hüseyin Budak
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Waewta Luangboon: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Kamsing Nonlaopon: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Jessada Tariboon: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Hüseyin Budak: Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey

Mathematics, 2022, vol. 10, issue 5, 1-20

Abstract: In this paper, we establish a new ( p , q ) b -integral identity involving the first-order ( p , q ) b -derivative. Then, we use this result to prove some new ( p , q ) b -integral inequalities related to Hermite–Hadamard inequalities for ( p , q ) b -differentiable convex functions. Furthermore, our main results are used to study some special cases of various integral inequalities. The newly presented results are proven to be generalizations of some integral inequalities of already published results. Finally, some examples are given to illustrate the investigated results.

Keywords: Hermite–Hadamard inequality; convex function; ( p , q )-differentiable function; ( p , q )-integral inequalities; ( p , q )-calculus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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