离散型Carlson's不等式的一些推广及改进

Some Extensions and Improvements of Discrete Carlson's Inequality

中文关键词:  无穷级数  Carlson不等式  Mathieu不等式

英文关键词:infinite series  Carlson's inequality  Mathieu's inequality

中文摘要:

      利用H"{o}lder不等式和实分析方法,得到了离散型Carlson不等式的两种推广形式.通过所得结果及一个无穷级数求和公式,给出了离散型Carlson不等式的一些改进并建立了一些与Mathieu 类型的无穷级数不等式等价的Carlson型不等式.最后通过一个积分不等式得到了Nagy-Hardy-Carlson级数不等式的一种改进.

英文摘要:

      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.