SOME NEW GENERALIZATIONS of HADAMARD-TYPE MIDPOINT INEQUALITIES INVOLVING FRACTIONAL INTEGRALS

Bayraktar B.

Problemy Analiza — Issues of Analysis, vol.9, no.27, pp.66-82, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 27
  • Publication Date: 2020
  • Doi Number: 10.15393/j3.art.2020.8270
  • Journal Name: Problemy Analiza — Issues of Analysis
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.66-82
  • Keywords: convexity, Hadamard inequality, Holder's inequality, Power-mean inequality, Riemann-Liouville fractional integrals
  • Bursa Uludag University Affiliated: Yes

Abstract

In this study, we formulate the identity and obtain some generalized inequalities of the Hermite-Hadamard type by using fractional Riemann-Liouville integrals for functions whose absolute values of the second derivatives are convex. The results are obtained by uniformly dividing a segment [a,b] into n equal sub-intervals. Using this approach, the absolute error of a Midpoint inequality is shown to decrease approximately n(2) times. A dependency between accuracy of the absolute error (epsilon) of the upper limit of the Hadamard inequality and the number (n) of lower intervals is obtained.