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

In: Approximation Theory and Analytic Inequalities

Author

Listed:
  • Artion Kashuri

    (University Ismail Qemali of Vlora, Faculty of Technical Science, Department of Mathematics)

  • Rozana Liko

    (University Ismail Qemali of Vlora, Faculty of Technical Science, Department of Mathematics)

Abstract

In this paper, the authors discover two interesting identities regarding Gauss–Jacobi and Hermite–Hadamard type integral inequalities. By using the first lemma as an auxiliary result, some new bounds with respect to Gauss–Jacobi type integral inequalities are established. Also, using the second lemma, some new estimates with respect to Hermite–Hadamard type integral inequalities via general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from main results. Some applications to special means for different positive real numbers and new error estimates for the trapezoidal formula are provided as well. These results give us the generalizations, refinement and significant improvements of the new and previous known results. The ideas and techniques of this paper may stimulate further research.

Suggested Citation

  • Artion Kashuri & Rozana Liko, 2021. "Some New Refinement of Gauss–Jacobi and Hermite–Hadamard Type Integral Inequalities," Springer Books, in: Themistocles M. Rassias (ed.), Approximation Theory and Analytic Inequalities, pages 227-250, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-60622-0_13
    DOI: 10.1007/978-3-030-60622-0_13
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