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Parameterized Inequalities of Different Types for Preinvex Functions with Respect to another Function via Generalized Fractional Integral Operators and their Applications

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Ukrainian Mathematical Journal Aims and scope

We prove an identity with two parameters for a function differentiable with respect to another function via generalized integral operator. By applying the established identity, we discover the generalized trapezium, midpoint, and Simpson-type integral inequalities. It is indicated that the results of the present research provide integral inequalities for almost all fractional integrals discovered in recent decades. Various special cases are identified. Some applications of the presented results to special means and new error estimates for the trapezium and midpoint quadrature formulas are analyzed. The ideas and techniques of the present paper may stimulate further research in the field of integral inequalities.

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Authors and Affiliations

  1. University Ismail Qemali, Vlora, Albania

    A. Kashuri

  2. Düzce University, Düzce, Turkey

    M. Z. Sarikaya

Authors
  1. A. Kashuri
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  2. M. Z. Sarikaya
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Correspondence to A. Kashuri.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 9, pp. 1181–1204, September, 2021. Ukrainian DOI: 10.37863/umzh.v73i9.805.

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Kashuri, A., Sarikaya, M.Z. Parameterized Inequalities of Different Types for Preinvex Functions with Respect to another Function via Generalized Fractional Integral Operators and their Applications. Ukr Math J 73, 1371–1397 (2022). https://doi.org/10.1007/s11253-022-02000-w

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  • DOI: https://doi.org/10.1007/s11253-022-02000-w

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