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On Hermite–Hadamard type inequalities for newly defined generalized quantum integrals

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Abstract

In this paper, we first introduce four new generalized quantum integrals of two variables functions which are called \(T_{q}\)-integrals. We also give some examples of each of these given integrals. Then we establish corresponding \(T_{q}\)-Hermite–Hadamard type inequalities for co-ordinated convex functions. In order to show correctness of our results, we apply our main theorems to several co-ordinated convex functions.

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Acknowledgements

The authors would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Natural and Applied Sciences, Düzce University, Düzce, Turkey

    Hasan Kara

  2. Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey

    Hüseyin Budak

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  1. Hasan Kara
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  2. Hüseyin Budak
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Kara, H., Budak, H. On Hermite–Hadamard type inequalities for newly defined generalized quantum integrals. Ricerche mat 73, 1145–1166 (2024). https://doi.org/10.1007/s11587-021-00662-5

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