Some new Hadamard-type inequalities via fractional integral operators Algunas nuevas desigualdades tipo Hadamard a través de operadores integrales fraccionarios

BAYRAKTAR B., Butt S. I., Kórus P.

Revista Colombiana de Matematicas, vol.59, no.1, pp.1-28, 2025 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.15446/recolma.v59n1.122851
  • Journal Name: Revista Colombiana de Matematicas
  • Journal Indexes: Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.1-28
  • Keywords: 26A51, 26D51, Convex functions, fractional calculus, Hadamard’s inequality, Hölder’s inequality, special functions
  • Bursa Uludag University Affiliated: Yes

Abstract

The article presents new inequalities of Hadamard-type which are obtained using fractional integral operators belonging to a function whose third-order derivative is convex. The proposed Hadamard-type inequalities have the potential for application in various areas where it is required to estimate the properties of functions with a convex third-order derivative. Examples of functions are given based on a comparative analysis of the estimates of the upper bounds of the Hadamard-type inequalities obtained using the classical and extended Hölder inequalities. Finally, applications to special functions are provided.