Newton-cotes quadrature formula for third differentiable and h-convex Functions

Abstract

This paper develops a novel Newton-cotes quadrature formula forthird-differentiable and $h$-convex functions using Riemann integrals.Furthermore, new Newton-type inequalities are proposed utilizing a summationparameter $p\geq1$ for $s$-convexity, convexity and $P$-functions class.