Bullen inequality for third differentiable functions

Benaissa B., Azzouz N., BUDAK H.

Filomat, vol.39, no.13, pp.4601-4612, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 13
  • Publication Date: 2025
  • Doi Number: 10.2298/fil2513601b
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4601-4612
  • Keywords: Bullen inequality, Hölder inequality, Riemann integral, s-convex function
  • Kocaeli University Affiliated: Yes

Abstract

This paper develops a novel Bullen inequality for third-differentiable functions using Riemann integrals. Furthermore, new Bullen inequalities are proposed utilizing a summation parameter p ≥ 1 for and s-convex functions,convex functions and P-functions classes. Particular cases are studied when the third derivative functions are also bounded and Lipschitzian.