Generalization of Hilbert's Integral Inequality

On a Generalization of Hilbert-Type Integral Inequality

A Generalization of Constantin’s Integral Inequality and Its Discrete Analogue

Received: 21 March, 2007 Accepted: 08 May, 2007 Communicated by: S.S. Dragomir 2000 AMS Sub. Class.: 26D10, 26D15, 39A12, 45D05.

Generalization on Kantorovich Inequality

In this paper, we provide a new form of upper bound for the converse of Jensen’s inequality. Thereby, known estimations of the difference and ratio in Jensen’s inequality are essentially improved. As an application, we also obtain an improvement of Kantorovich inequality.

A Generalization of Hilbert’s Inequality

In a generalization of the classical Hilbert inequality by Hardy, Littlewood and Pólya, the best constant for an inequality is determined provided that the generating function for the corresponding matrix satisfies certain monotonicity condition. In this paper, we determine the best constant for a class of inequalities when the monotonicity condition is no longer satisfied. Mathematics subject ...

Next generalization of Cîrtoaje’s inequality

In this paper, we classify sets of solutions of the next generalized Cîrtoaje's inequality and its reverse, respectively.