# On a $q$-analogue of the Hilbert's type inequality

Volume 11, Issue 11, pp 1243--1249 Publication Date: August 27, 2018       Article History
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### Authors

Zhengping Zhang - College of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing, 401331, P. R. China. Gaowen Xi - College of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing, 401331, P. R. China.

### Abstract

In this paper, by introducing a parameter $q$ and using the expression of the beta function establishing the inequality of the weight coefficient, we give a $q$-analogue of the Hilbert's type inequality. As applications, a generalization of Hardy-Hilbert's inequality are obtained.

### Keywords

• $q$-Analogue
• Hilbert's type inequality
• weight coefficient
• Holder inequality
• generalization

•  05A30
•  26D15

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