关于加权均值的凯德莱亚型不等式。
On Kedlaya-type inequalities for weighted means.
作者信息
Páles Zsolt, Pasteczka Paweł
机构信息
1Institute of Mathematics, University of Debrecen, Debrecen, Hungary.
2Institute of Mathematics, Pedagogical University of Cracow, Cracow, Poland.
出版信息
J Inequal Appl. 2018;2018(1):99. doi: 10.1186/s13660-018-1685-z. Epub 2018 Apr 25.
In 2016 we proved that for every symmetric, repetition invariant and Jensen concave mean [Formula: see text] the Kedlaya-type inequality [Formula: see text] holds for an arbitrary [Formula: see text] ([Formula: see text] stands for the arithmetic mean). We are going to prove the weighted counterpart of this inequality. More precisely, if [Formula: see text] is a vector with corresponding (non-normalized) weights [Formula: see text] and [Formula: see text] denotes the weighted mean then, under analogous conditions on [Formula: see text], the inequality [Formula: see text] holds for every [Formula: see text] and [Formula: see text] such that the sequence [Formula: see text] is decreasing.
2016年，我们证明了对于每一个对称、重复不变且詹森凹平均[公式：见正文]，对于任意的[公式：见正文]（[公式：见正文]表示算术平均），凯德莱亚型不等式[公式：见正文]成立。我们将证明这个不等式的加权形式。更确切地说，如果[公式：见正文]是一个向量，其对应的（未归一化）权重为[公式：见正文]，并且[公式：见正文]表示加权平均，那么在对[公式：见正文]的类似条件下，对于每一个[公式：见正文]和[公式：见正文]，使得序列[公式：见正文]递减时，不等式[公式：见正文]成立。
Zotero 插件