A study of Milne-type inequalities for several convex function classes with applications

Munir A., Qayyum A., Budak H., Faiz I., Kara H., Supadi S. S.

FILOMAT, vol.38, no.32, pp.11539-11551, 2024 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 32
  • Publication Date: 2024
  • Doi Number: 10.2298/fil2432539m
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.11539-11551
  • Kocaeli University Affiliated: No

Abstract

Fractional integral operators have indeed been the subject of significant research in various mathematical and scientific disciplines over the past few decades. The main aim of this article is to establish a new identity employing the Atangana Baleanu fractional integral operator for the case of differentiable functions. Moreover, we present several fractional Milne-type inequalities for bounded function by fractional integrals. Furthermore, we obtain fractional Milne-type inequalities for the case of Lipschitzian functions. Lastly, we explore applications related to special means, and quadrature formulas.