• 제목/요약/키워드: Milne-type inequalities

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A STUDY ON MILNE-TYPE INEQUALITIES FOR A SPECIFIC FRACTIONAL INTEGRAL OPERATOR WITH APPLICATIONS

  • Arslan Munir;Ather Qayyum;Laxmi Rathour;Gulnaz Atta;Siti Suzlin Supadi;Usman Ali
    • Korean Journal of Mathematics
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    • 제32권2호
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    • pp.297-314
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    • 2024
  • Fractional integral operators have been studied extensively in the last few decades by various mathematicians, because it plays a vital role in the developments of new inequalities. The main goal of the current study is to establish some new Milne-type inequalities by using the special type of fractional integral operator i.e Caputo Fabrizio operator. Additionally, generalization of these developed Milne-type inequalities for s-convex function are also given. Furthermore, applications to some special means, quadrature formula, and q-digamma functions are presented.

MILNE TYPE INEQUALITIES FOR DIFFERENTIABLE s-CONVEX FUNCTIONS

  • Djenaoui, Meriem;Meftah, Badreddine
    • 호남수학학술지
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    • 제44권3호
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    • pp.325-338
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    • 2022
  • In this paper, a new identity is given. On the basis of this identity, we establish some new estimates of Milne's quadrature rule, for functions whose first derivative is s-convex. We discuss the cases where the derivatives are bounded as well as Lipschitzian. Some illustrative applications are given.