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In this study, new inequalities have been obtained by employing a generalized fractional integral operator which generalizes some fractional integral operators existing in the literature. In the initial step of the study, certain general properties related to Grüss and Chebyshev inequalities were discussed, followed by establishing a hierarchy among some fractional integral operators already existing in the literature. In the main results section, new lemmas and inequalities of Grüss and Chebyshev type have been obtained using the aforementioned fractional integral operator.

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Some New Chebyshev and Grüss-Type Fractional Inequalities Obtained by a Generalized Fractional Integral Operator

  • 会议论文

  • 发表日期：

    2025年

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  • Mustafa Gürbüz,
  • Çağrı Aşak

摘要

In this study, new inequalities have been obtained by employing a generalized fractional integral operator which generalizes some fractional integral operators existing in the literature. In the initial step of the study, certain general properties related to Grüss and Chebyshev inequalities were discussed, followed by establishing a hierarchy among some fractional integral operators already existing in the literature. In the main results section, new lemmas and inequalities of Grüss and Chebyshev type have been obtained using the aforementioned fractional integral operator.