Advanced Hermite-Hadamard-Mercer Type Inequalities with Refined Error Estimates and Applications

Munir A., BUDAK H., Kashuri A., Ciurdariu L.

Fractal and Fractional, cilt.10, sa.1, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3390/fractalfract10010071
  • Dergi Adı: Fractal and Fractional
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, Directory of Open Access Journals
  • Anahtar Kelimeler: bounded function, fractional integral operators, Hermite–Hadamard–Mercer-type inequality, Hölder’s inequality, L-Lipschitzian function, midpoint formula, modified Bessel function, power–mean inequality, q-digamma function, s-convex function, special means, Young’s inequality
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

The purpose of this research is to develop a set of Hermite–Hadamard–Mercer-type inequalities that involve different types of fractional integral operators such as classical Riemann–Liouville fractional integral operators. Furthermore, some fractional integral inequalities are obtained for three-times differentiable convex functions with respect to the right-hand side of the Hermite–Hadamard–Mercer-type inequality. Moreover, several new results regarding Young’s inequality, bounded function and L-Lipschitzian function are deduced. The paper presents additional remarks and comments on the results to make sense of them. To illustrate the key findings, graphical representations are provided, and applications involving special means, midpoint formula, q-digamma function and modified Bessel function are presented to demonstrate the practical utility of the derived inequalities.