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

Bayraktar B.

Problemy Analiza — Issues of Analysis, cilt.9, sa.27, ss.66-82, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 27
  • Basım Tarihi: 2020
  • Doi Numarası: 10.15393/j3.art.2020.8270
  • Dergi Adı: Problemy Analiza — Issues of Analysis
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.66-82
  • Anahtar Kelimeler: convexity, Hadamard inequality, Holder's inequality, Power-mean inequality, Riemann-Liouville fractional integrals
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.