By the use of the weight coefficients, the idea of introducing parameters and the Euler-Maclaurin summation formula, a reverse extended Hardy-Hilbert inequality and the equivalent forms are given. The equivalent statements of the best possible constant factor related to a few parameters and some particular cases are also considered. MSC: 26D15

By means of weight coefficients and techniques of real analysis, a new Hardy-Hilbert-type inequality with multiparameters and the best possible constant factor is given. The equivalent forms, the operator expression with the norm, and the reverse and some particular inequalities with the best possible constant factors are also considered. MSC: 26D15; 47A07

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In this paper, by the use of the way of weight coefficients, the transfer formula, and the technique of real analysis, we introduce some proper parameters and obtain a multidimensional Hilbert-type inequality with the following kernel:and a best possible constant factor. The equivalent form, the operator expressions with the norm, and some particular cases are also considered. The lemmas and theorems provide an extensive account of this type of inequalities. MSC: 26D15; 47A07

By means of weight coefficients and the technique of real analysis, a new Hardy-Mulholland-type inequality with the kernel) and a best possible constant factor is provided, which is a relation between two simple Hardy-Mulholland-type inequalities with parameters. The equivalent forms, the operator expression with the norm, and some particular inequalities are studied. The lemmas and theorems of this paper provide an extensive account of this type of inequalities. MSC: 26D15; 47A07