Honam Mathematical Journal (호남수학학술지)

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ON RESULTS OF MIDPOINT-TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL OPERATORS WITH TWICE-DIFFERENTIABLE FUNCTIONS

  • Fatih Hezenci (Department of Mathematics, Faculty of Science and Arts, Duzce University) ;
  • Huseyin Budak (Department of Mathematics, Faculty of Science and Arts, Duzce University)
  • Received : 2022.12.19
  • Accepted : 2023.01.13
  • Published : 2023.06.01
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Abstract

This article establishes an equality for the case of twice-differentiable convex functions with respect to the conformable fractional integrals. With the help of this identity, we prove sundry midpoint-type inequalities by twice-differentiable convex functions according to conformable fractional integrals. Several important inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Using the specific selection of our results, we obtain several new and well-known results in the literature.

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References

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