ON GENERALIZATIONS OF INTEGRAL INEQUALITIES

Creative Commons License

BAYRAKTAR B., Nápoles J., Rabossi F.

Problemy Analiza, vol.12-29, no.2, pp.3-23, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 12-29 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.15393/j3.art.2022.11190
  • Journal Name: Problemy Analiza
  • Journal Indexes: Scopus
  • Page Numbers: pp.3-23
  • Keywords: Convex function, Hermite–hadamard inequality, Lagrange theorem, Lipschitz conditions, Riemann– liouville fractional integral, Simpson-type inequality
  • Bursa Uludag University Affiliated: Yes

Abstract

© Petrozavodsk State University, 2022In the present study, several new generalized integral inequalities of the Hadamard and Simpson-type are obtained. The results were obtained for functions whose first and third derivatives are either convex or satisfy the Lipschitz condition or the conditions of the Lagrange theorem. In a particular case, these results not only confirm but also improve some upper bounds, well known in the literature for the Simpson and Hermite-Hadamard-type inequalities.