Parameterized inequalities based on three times differentiable functions

Benaissa B., Azzouz N., Budak H.

BOUNDARY VALUE PROBLEMS, cilt.2025, sa.1, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2025 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1186/s13661-025-02032-8
  • Dergi Adı: BOUNDARY VALUE PROBLEMS
  • Derginin Tarandığı İndeksler: 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
  • Anahtar Kelimeler: Bounded function, Convex function, Function of bounded variation, Hermite–Hadamard inequality, Hölder inequality, Lipschitzian function
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.