Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus

Tariboon, Jessada; Ali, Muhammad Aamir; Budak, Hüseyin; Ntouyas, Sotiris K.

doi:10.3390/sym13071216

Open AccessArticle

Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus

¹

Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

²

Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

³

Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey

⁴

Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

⁵

Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

^*

Authors to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Symmetry 2021, 13(7), 1216; https://doi.org/10.3390/sym13071216

Submission received: 5 June 2021 / Revised: 30 June 2021 / Accepted: 3 July 2021 / Published: 7 July 2021

(This article belongs to the Special Issue Functional Equations and Inequalities 2021)

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Abstract

In this paper, the notions of post-quantum integrals for two-variable interval-valued functions are presented. The newly described integrals are then used to prove some new Hermite–Hadamard inclusions for co-ordinated convex interval-valued functions. Many of the findings in this paper are important extensions of previous findings in the literature. Finally, we present a few examples of our new findings. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.

Keywords: Hermite–Hadamard inequality; Hermite–Hadamard inclusion; (p, q)-integral; quantum calculus; co-ordinated convexity; interval-valued functions

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MDPI and ACS Style

Tariboon, J.; Ali, M.A.; Budak, H.; Ntouyas, S.K. Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus. Symmetry 2021, 13, 1216. https://doi.org/10.3390/sym13071216

AMA Style

Tariboon J, Ali MA, Budak H, Ntouyas SK. Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus. Symmetry. 2021; 13(7):1216. https://doi.org/10.3390/sym13071216

Chicago/Turabian Style

Tariboon, Jessada, Muhammad Aamir Ali, Hüseyin Budak, and Sotiris K. Ntouyas. 2021. "Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus" Symmetry 13, no. 7: 1216. https://doi.org/10.3390/sym13071216

APA Style

Tariboon, J., Ali, M. A., Budak, H., & Ntouyas, S. K. (2021). Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus. Symmetry, 13(7), 1216. https://doi.org/10.3390/sym13071216

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus

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