ON THE GENERAL FORM OF DISCRETE HILBERT-TYPE INEQUALITY

In this paper, we first construct a general discrete kernel function with several parameters, and then we establish a new discrete Hilbert-type inequality by using the method of weight coefficient and Euler-Maclaurin summation formula. Furthermore, the equivalent Hardy-type inequalities are also considered, and all the constant factors in the newly obtained inequalities are proved to be the best possible. At last, by assigning some specific functions to the new kernel, and using techniques of real analysis and the numerical calculation function of Matlab, some special Hilbert-type inequalities are established at the end of the paper.