Inequalities of Bullen's Type for Logarithmically Convexity With Numerical Applications

Abstract

In this study, we consider a familier inequality of Hermite-Hadamard inequality that is well known as Bullen's inequality in the literature. We remind an integral identity that derives Bullen's type integral inequalities. By using this integral identity, we have established new Bullen's type inequalities for functions whose second derivatives in absolute value are logarithmically convex. So, new error bounds for averaged midpoint-trapezoid quadrature rules are obtained and applications in numerical integration are given.