Parameterized inequalities based on three times differentiable functions

Benaissa B., Azzouz N., Budak H.

Boundary Value Problems, vol.2025, no.1, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2025 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1186/s13661-025-02032-8
  • Journal Name: Boundary Value Problems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Bounded function, Convex function, Function of bounded variation, Hermite–Hadamard inequality, Hölder inequality, Lipschitzian function
  • Kocaeli University Affiliated: Yes

Abstract

This paper presents a general identity including two real parameters for three times differentiable functions. By using this equality, we prove several inequalities by using diverse function classes such as convex function, bounded function, Lipschitzian function, and function of bounded variation. By special choices of the parameters in the obtained results, we present some well-known inequalities: midpoint inequality, trapezoid inequality, Milne inequality, Bullen inequality, and Simpson inequality.