On some Newton's type inequalities for differentiable convex functions via Riemann-Liouville fractional integrals


Ali M. A., Budak H., Feckan M., Patanarapeelert N., Sitthiwirattham T.

FILOMAT, vol.37, no.11, pp.3427-3441, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 11
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2311427a
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3427-3441
  • Kocaeli University Affiliated: No

Abstract

In this paper, we establish a new integral identity involving Riemann-Liouville fractional integrals and differentiable functions. Then, we use the newly established identity and prove several Newton's type inequalities for differentiable convex functions and functions of bounded variation. Moreover, we give a mathematical example and graphical analysis of newly established inequalities to show their validity.