Some generalized Hadamard type inequalities via fractional integrals


BAYRAKTAR B., Attaev A., Kudaev V.

Russian Mathematics, vol.65, no.2, pp.1-14, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 65 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.3103/s1066369x21020018
  • Journal Name: Russian Mathematics
  • Journal Indexes: Emerging Sources Citation Index, Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.1-14
  • Keywords: convex functions, s-convex functions, Hadamard inequality, H&#246, lder inequality, power-mean inequality, Riemann&#8211, Liouville fractional integrals

Abstract

In this paper, we establish some generalized inequalities of the Hermite-Hadamard type using fractional Riemann-Liouville integrals for the class of s-convex functions in the first and second sense. We assume that second derivatives of these functions are convex and take on values at intermediate points of the interval under consideration. We prove that this approach reduces the absolute error of Hadamard-type inequalities by a multiple of the number of intermediate points. In a particular case, the obtained upper bounds for the Hadamard inequality coincide with those given in the literature.