Some generalized Hadamard type inequalities via fractional integrals

BAYRAKTAR B., Attaev A., Kudaev V.

Russian Mathematics, cilt.65, sa.2, ss.1-14, 2021 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3103/s1066369x21020018
  • Dergi Adı: Russian Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1-14
  • Anahtar Kelimeler: convex functions, s-convex functions, Hadamard inequality, H&#246, lder inequality, power-mean inequality, Riemann&#8211, Liouville fractional integrals
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.