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Some New Estimates for Integral Inequalities and Their Applications

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We obtain several new integral inequalities in terms of fractional integral operators for the functions whose first derivatives satisfy either the conditions of the Lagrange theorem or the Lipschitz condition. In some special cases, the obtained results provide better upper estimates than the results known in the literature for the Bullen-type inequality and the Hadamard-type right-hand side inequality. Finally, some error estimates for the trapezoidal formula are discussed.

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Authors and Affiliations

  1. Faculty of Education, Bursa Uludag University, Gorukle Campus, Bursa, Turkey

    B. Bayraktar

  2. COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan

    S. I. Butt

  3. UNNE, FaCENA, Corrientes, Argentina

    J. E. Nápoles

  4. UTN-FRRE, Resistencia, Chaco, Argentina

    J. E. Nápoles & F. Rabossi

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  1. B. Bayraktar
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Correspondence to B. Bayraktar.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, No. 2, pp. 159–178, February, 2024. Ukrainian DOI: https://doi.org/10.3842/umzh.v76i2.7266.

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Bayraktar, B., Butt, S.I., Nápoles, J.E. et al. Some New Estimates for Integral Inequalities and Their Applications. Ukr Math J 76, 169–191 (2024). https://doi.org/10.1007/s11253-024-02315-w

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