Hermite–Hadamard–Mercer’s-type inequalities for h-convex function

Shehzadi A., Chen H., BUDAK H., Haider W., Ali M. A.

Filomat, vol.39, no.18, pp.6367-6381, 2025 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 18
  • Publication Date: 2025
  • Doi Number: 10.2298/fil2518367a
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.6367-6381
  • Keywords: Convex function, h-convex function, Hermite–Hadamard-Mercer-type inequalities, Jensen–Mercer inequality
  • Kocaeli University Affiliated: No

Abstract

In this paper, we prove significant results related to the Hermite–Hadamard–Mercer-type inequality for h-convex functions in the framework of Katugampola fractional integral operators. Also, we establish some novel fractional inequalities related to the right and left sides of Hermite–Hadamard–Mercer-type inequalities for differentiable mappings whose derivatives in absolute value are h-convex function. The findings in this research generalise a number of inequities identified in earlier studies.