论文标题
微积分的不平等：提出结果和解决问题的方法
Inequalities in calculus: methods of prooving results and problem solving
论文作者
论文摘要
该预印本是针对学生和老师的不平等文本。一些标准主题涵盖了将微积分应用于不平等的证明。考虑了许多示例，陈述，解决或部分解决。有些问题是标准的，但有些是罕见的，新的和原始的。 The next topics are considered with many examples: monotonicity of functions, Lagrange theorem and inequalities proving, estimating of finite sums, inequalities of Schlömilch-LeMonnier type, proof of inequalities by method of mathematical induction, inequalities for the number $e$, exponentials, logarithmic and similar functions, some means and their inequalities, Cauchy-Bunyakovskii，Minkovskii，Young，Hölder（Rogers-Hölder-Riesz！）不平等及其一些改进和概括。一些新的结果包括对指数，对数和类似功能的不平等，Cauchy-Bunyakovskii的概括和年轻的不平等，有些平均不平等现象，包括复杂域名的平均不平等等等。
This preprint is a text for students and teachers on inequalities. Some standard topics are covered on application of calculus to inequality proving. Many examples are considered, stated, solved or partially solved. Some problems are standard, but some are rare, new and original. The next topics are considered with many examples: monotonicity of functions, Lagrange theorem and inequalities proving, estimating of finite sums, inequalities of Schlömilch-LeMonnier type, proof of inequalities by method of mathematical induction, inequalities for the number $e$, exponentials, logarithmic and similar functions, some means and their inequalities, Cauchy-Bunyakovskii, Minkovskii, Young, Hölder (Rogers-Hölder-Riesz !) inequalities and some of their improvements and generalisations. Some new results include inequalities on exponentials, logarithmic and similar functions, generalisations of Cauchy--Bunyakovskii and Young inequalities, some mean inequalities including mean inequalities on the complex domain and more.
