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Volume 7, Issue 5
Some Hermite-Hadamard Type Inequalities with the Aid of Newly Defined Double Post-Quantum Integrals

Hasan Kara, Hüseyin Budak, Fatih Hezenci & Muhammad Uzair Awan

DOI: 10.12150/jnma.2025.1683

J. Nonl. Mod. Anal., 7 (2025), pp. 1683-1703.

Published online: 2025-09

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In the present paper, we first give four post-quantum integrals for functions of two variables, denoted by $_{ac}T_{p,q},$ $^d_ aT_{p,q},$ $^b_cT_{p,q}$ 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.

  • Keywords

Hermite-Hadamard inequality, $q$-integral, $T_q$-integral, quantum calculus, co-ordinated convexity.

  • AMS Subject Headings

26D15, 26B20, 26D10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1683, author = {Kara , HasanBudak , HüseyinHezenci , Fatih and Awan , Muhammad Uzair}, title = {Some Hermite-Hadamard Type Inequalities with the Aid of Newly Defined Double Post-Quantum Integrals}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {5}, pages = {1683--1703}, abstract = {

In the present paper, we first give four post-quantum integrals for functions of two variables, denoted by $_{ac}T_{p,q},$ $^d_ aT_{p,q},$ $^b_cT_{p,q}$ 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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1683}, url = {http://global-sci.org/intro/article_detail/jnma/24384.html} }
TY - JOUR T1 - Some Hermite-Hadamard Type Inequalities with the Aid of Newly Defined Double Post-Quantum Integrals AU - Kara , Hasan AU - Budak , Hüseyin AU - Hezenci , Fatih AU - Awan , Muhammad Uzair JO - Journal of Nonlinear Modeling and Analysis VL - 5 SP - 1683 EP - 1703 PY - 2025 DA - 2025/09 SN - 7 DO - http://doi.org/10.12150/jnma.2025.1683 UR - https://global-sci.org/intro/article_detail/jnma/24384.html KW - Hermite-Hadamard inequality, $q$-integral, $T_q$-integral, quantum calculus, co-ordinated convexity. AB -

In the present paper, we first give four post-quantum integrals for functions of two variables, denoted by $_{ac}T_{p,q},$ $^d_ aT_{p,q},$ $^b_cT_{p,q}$ 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.

Kara , HasanBudak , HüseyinHezenci , Fatih and Awan , Muhammad Uzair. (2025). Some Hermite-Hadamard Type Inequalities with the Aid of Newly Defined Double Post-Quantum Integrals. Journal of Nonlinear Modeling and Analysis. 7 (5). 1683-1703. doi:10.12150/jnma.2025.1683
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