Two sharp inequalities are derived. The first of them is a sharp inequality which gives an error bound for a Gauss-Legendre quadrature rule. The second is a sharp inequality which gives an error bound for a Radau quadrature rule. These inequalities enlarge the applicability of the corresponding quadrature rules with respect to the obtained error bounds. Applications in numerical integration are also given.
"TWO SHARP OSTROWSKI-LIKE INEQUALITIES AND APPLICATIONS." Methods Appl. Anal. 10 (3) 477 - 486, Sept 2003.