Weighted Hermite–Hadamard integral inequalities for general convex functions

Kórus P., Valdés J. E. N., Bayraktar B.

Mathematical Biosciences and Engineering, vol.20, no.11, pp.19929-19940, 2023 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 11
  • Publication Date: 2023
  • Doi Number: 10.3934/mbe.2023882
  • Journal Name: Mathematical Biosciences and Engineering
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, BIOSIS, Compendex, MEDLINE, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.19929-19940
  • Keywords: convex functions, general convex functions, Hermite–Hadamard inequality, weighted integral operators
  • Bursa Uludag University Affiliated: Yes

Abstract

In this article, starting with an equation for weighted integrals, we obtained several extensions of the well-known Hermite–Hadamard inequality. We used generalized weighted integral operators, which contain the Riemann–Liouville and the k-Riemann–Liouville fractional integral operators. The functions for which the operators were considered satisfy various conditions such as the h-convexity, modified h-convexity and s-convexity.