On Ostrowski-type inequalities for higher-order partial derivatives.
Let be a real number and let be an even integer. We determine the largest value such that the inequality holds for all real numbers which are pairwise distinct and satisfy . Our theorem completes results of Ozeki, Mitrinović-Kalajdžić, and Russell, who found the optimal value in the case and odd, and in the case and even.
In this paper we obtain certain refinements (and new proofs) for inequalities involving means, results attributed to Carlson; Leach and Sholander; Alzer; Sndor; and Vamanamurthy and Vuorinen.
In this paper we establish some new nonlinear difference inequalities. We also present an application of one inequality to certain nonlinear sum-difference equation.