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Some New Bounds of Gauss–Jacobi and Hermite–Hadamard-Type Integral Inequalities

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Ukrainian Mathematical Journal Aims and scope

We deduce two interesting identities for the Gauss–Jacobi and Hermite–Hadamard-type integral inequalities. By using the first lemma as an auxiliary result, we establish some new bounds for the Gauss–Jacobi type integral inequalities. Moreover, by using the second lemma, we obtain some new estimates for the Hermite–Hadamard-type integral inequalities via general fractional integrals. It is indicated that some new special cases can be deduced from the main results. Some applications to special means for different positive real numbers and new error estimates for the trapezoidal method are also provided. These results give us generalizations, refinements, and significant improvements of some new and previous known results. The ideas and techniques used in the paper may stimulate further research into this field.

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Authors and Affiliations

  1. University Ismail Qemali, Vlora, Albania

    A. Kashuri, M. Ramosaçaj & R. Liko

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  1. A. Kashuri
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  2. M. Ramosaçaj
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  3. R. Liko
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Correspondence to A. Kashuri.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 8, pp. 1067–1084, August, 2021. Ukrainian DOI: 10.37863/umzh.v73i8.603.

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Kashuri, A., Ramosaçaj, M. & Liko, R. Some New Bounds of Gauss–Jacobi and Hermite–Hadamard-Type Integral Inequalities. Ukr Math J 73, 1238–1258 (2022). https://doi.org/10.1007/s11253-022-01997-4

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  • DOI: https://doi.org/10.1007/s11253-022-01997-4

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