A Hermite–Hadamard type inequality with applications to the estimation of moments of continuous random variables

• We present a new Hadamard-type inequality for quasi-convex functions.
• Our results have applications to the estimation of moments of random variables.
• Our work generalizes some recent results published in 2014 in AMC.

In this paper we present a Hadamard-type inequality for quasi-convex functions with applications to the estimation of moments of continuous random variables with compact support. The main result obtained here generalizes the inequality obtained by Alomari et al. (2010).