Symmetry (Mar 2021)

Midpoint Inequalities in Fractional Calculus Defined Using Positive Weighted Symmetry Function Kernels

  • Pshtiwan Othman Mohammed,
  • Hassen Aydi,
  • Artion Kashuri,
  • Y. S. Hamed,
  • Khadijah M. Abualnaja

DOI
https://doi.org/10.3390/sym13040550
Journal volume & issue
Vol. 13, no. 4
p. 550

Abstract

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The aim of our study is to establish, for convex functions on an interval, a midpoint version of the fractional HHF type inequality. The corresponding fractional integral has a symmetric weight function composed with an increasing function as integral kernel. We also consider a midpoint identity and establish some related inequalities based on this identity. Some special cases can be considered from our main results. These results confirm the generality of our attempt.

Keywords