Weighted Hermite–Hadamard integral inequalities for general convex functions

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.

Keywords

• weighted integral operators
• convex functions
• general convex functions
• hermite–hadamard inequality