Hermite-Hadamard type inequalities for new class h-convex mappings utilizing weighted generalized fractional integrals

Benaissa B., Azzouz N., BUDAK H., Erden S.

Mathematica Slovaca, cilt.75, sa.4, ss.791-806, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 75 Sayı: 4
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1515/ms-2025-0058
  • Dergi Adı: Mathematica Slovaca
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.791-806
  • Anahtar Kelimeler: (k, ψ)-Hilfer operators, B-function, h-convex function, Hermite-Hadamard inequality, midpoint inequality, trapezoid inequality, weighted inequalities
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this paper, we first introduce the fractional integral operators of a function with respect to another function. Then, we prove a new version of Hermite-Hadamard for newly introduced fractional integral operators. For this aim, we use the h-convex function in the case the function h is a B-function. Moreover, we also establish several corresponding trapezoid and midpoint type inequalities by using h-convex function and Hölder inequality.