New quantum Hermite–Hadamard-type inequalities for $p$-convex functions involving recently defined quantum integrals

Ghazala Gulshan; Hüseyin Budak; Rashida Hussain; Muhammad Aamir Ali

doi:10.3842/umzh.v75i9.7200

Ghazala Gulshan Department of Mathematics, Faculty of Science, Mirpur University of Science and Technology (MUST), Pakistan
Hüseyin Budak Department of Mathematics, Faculty of Science and Arts, Düzce University, Turkey
Rashida Hussain Department of Mathematics, Faculty of Science, Mirpur University of Science and Technology (MUST), Pakistan
Muhammad Aamir Ali Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, China

DOI: https://doi.org/10.3842/umzh.v75i9.7200

Keywords: Hermite-Hadamard inequality, $p$-convex functions, co-ordinated $p$- convex functions, $_a{T_{q}}$-integral, $^b{T_{q}}$ integral.

Abstract

UDC 517.5

We develop new Hermite–Hadamard-type integral inequalities for $p$-convex functions in the context of $q$-calculus by using the concept of recently defined $T_{q}$-integrals. Then thе obtained Hermite–Hadamard inequality for $p$-convex functions is used to get new Hermite–Hadamard inequality for coordinated $p$-convex functions. Furthermore, we present some examples to demonstrate the validity of our main results. We hope that the ideas and techniques of this study may stimulate further research in this field.

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