Open two-point Newton-Cotes integral inequalities for differentiable convex functions via Riemann-Liouville fractional integrals

Hamida Ayed\(^{a,b}\), Badreddine Meftah\(^{c,*}\)

\(^a\)Universit´e Larbi Tebessi. T´ebessa 12000

\(^b\)Laboratoire des Surfaces et Interfaces des Couches Minces (LECIMS) universit´e Badji Mokhtar Annaba 23000

\(^c\)D´epartement des Math´ematiques, Facult´e des math´ematiques, de l’informatique et des sciences de la mati`ere, Universit´e 8 mai 1945 Guelma, Algeria

Correspondence should be addressed to: hamida.ayed@univ-tebessa.dz, ayedhami@yahoo.fr, badrimeftah@yahoo.fr

Copyright © 2023 Hamida Ayed, Badreddine Meftah . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 20 September 2022; Accepted: 06 January 2023; Published Online: 26 September 2023.

Abstract

In this paper, some open two-point Newton-Cotes type integral inequalities for functions whose first derivatives are convex via Riemann-Liouville fractional integrals are established. Our finding generalize some already known results. In order to illustrate the efficiency of our main results, some applications are given.

Keywords:

Riemann-Liouville fractional integrals, convex functions, H¨older inequality, discrete power mean inequality.