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| Some Hermite-Hadamard Type Inequalities with the Aid of Newly Defined Double Post-Quantum Integrals |
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| KeyWord:Hermite-Hadamard inequality, $q$-integral, $T_{q}$-integral, quantum calculus, co-ordinated convexity |
| Author Name | Affiliation | | Hasan Kara | Department of Mathematics, Faculty of Science and Arts, Duzce University, T\"{u}rkiye | | H\"{u}seyin Budak | Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai 602105, Tamil Nadu, India
Department of Mathematics, Faculty of Sciences and Art, Kocaeli University, Kocaeli 41001, T\"{u}rkiye | | Fatih Hezenci | Department of Mathematics, Faculty of Science and Arts, Duzce University, T\"{u}rkiye | | Muhammad Uzair Awan | Department of Mathematics, Government College University, Faisalabad, Pakistan |
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| Abstract: |
| In the present paper, we first give four post-quantum integrals for functions of two variables, denoted by $_{ac}T_{p,q}$, $_{a}^{d}T_{p,q},$ $%_{c}^{b}T_{p,q}$ and $^{bd}T_{p,q}$. Afterwards, each of these newly defined integrals is illustrated. Moreover, some new Hermite-Hadamard inequalities are established based on these definitions. We also show the correctness of these inequalities with the aid of some numerical examples. |
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