In this paper, we derive a new discrete Hilbert-type inequality involving partial sums. Moreover, we show that the constant on the right-hand side of this inequality is the best possible. As an application, we consider some particular settings.

In this paper we introduce some new forms of the Hilbert integral inequality, and we study the connection between the obtained inequalities with Hardy inequalities. The reverse form and some applications are also given. MSC: 26D15

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In this paper by estimating the triple integral ∞ 0 ∞ 0 ∞ 0 f (x,y)g(z)(x+y+z) λ dxdydz , we introduce a new form of the Hilbert inequality for three variables with a best constant factor. The reverse form and some equivalent forms are also considered.Mathematics subject classification (2010): 26D15, 47A07.

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