Some Extensions and Improvements of Discrete Carlson's Inequality |
Received:October 24, 2014 Revised:January 16, 2015 |
Key Words:
infinite series Carlson's inequality Mathieu's inequality
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Abstract: |
In this paper, we consider Carlson type inequalities and discuss their possible improvement. First, we obtain two different types of generalizations of discrete Carlson's inequality by using the H\"{o}lder inequality and the method of real analysis, then we combine the obtained results with a summation formula of infinite series and some Mathieu type inequalities to establish some improvements of discrete Carlson's inequality and some Carlson type inequalities which are equivalent to the Mathieu type inequalities. Finally, we prove an integral inequality that enables us to deduce an improvement of the Nagy-Hardy-Carlson inequality. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2016.01.008 |
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