论文标题
关于离散和整体cauchy-bunyakovskii不平等的概括，通过平均值的方法。一些应用程序
On generalizations of discrete and integral Cauchy-Bunyakovskii inequalities by the method of mean values. Some applications
论文作者
论文摘要
在此预印本中，我们考虑了通过平均值和某些应用的平均值方法进行离散和积分Cauchy-bunyakovskii不平等的概括。大多数情况下，该材料是简短的调查，但证明了一些结果。列出了主要结果，其中包括具有最大和最小值的有趣不平等。从数学的不同领域考虑了一些应用程序。其中包括对某些特殊功能的估计，包括Euler Gamma和不完整的伽马函数，这是第一种的Legendre完整椭圆积分。同样，考虑和概述了一些进一步的概括，包括Aczél和Minkovskii不平等的概括，这是一种带有标志性形式的空间的情况，即杰克逊的$ Q $ integrals。
In this preprint we consider generalizations of discrete and integral Cauchy--Bunyakovskii inequalities by the method of mean values with some applications. Mostly the material is compiled as a short survey but some results are proved. Main results are listed, including an interesting inequality with maximum and minimum values. Some applications are considered from different fields of mathematics. Among them are estimates for some special functions, including Euler gamma and incomplete gamma function, the Legendre complete elliptic integrals of the first kind. Also some further possible generalizations are considered and outlined, including generalizations of the Aczél and Minkovskii inequalities, a case of spaces with sign-indefinite form, the Jackson's $q$-integrals.
