Hermite-Hadamard-Mercer type inequalities for fractional integrals: A study with <i>h</i>-convexity and <i>ψ</i>-Hilfer operators

Azzouz N., Benaissa B., Budak H., Demir I.

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/s13661-025-02001-1
  • 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
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

In this paper, we first prove a generalized fractional version of Hermite-Hadamard-Mercer type inequalities using h-convex functions by means of psi-Hilfer fractional integral operators. Then, we give new identities of this type with special functions depending on psi. Moreover, we establish some new fractional integral inequalities connected with the right- and left-hand sides of Hermite-Hadamard-Mercer inequalities involving differentiable mappings whose absolute values of the derivatives are h-convex. For the development of these novel integral inequalities, we utilize h-Mercer inequality and H & ouml;lder's integral inequality. These results offer the significant advantage of being convertible into classical integral inequalities and Riemann-Liouville fractional integral inequalities for convex functions, s-convex functions, and P-convex functions.