论文标题
通过基本不平等和衍生物的平均值定理的Young积分不平等的改进
Refinements of Young's integral inequality via fundamental inequalities and mean value theorems for derivatives
论文作者
论文摘要
In the paper, the authors review several refinements of Young's integral inequality via several mean value theorems, such as Lagrange's and Taylor's mean value theorems of Lagrange's and Cauchy's type remainders, and via several fundamental inequalities, such as Čebyšev's integral inequality, Hermite--Hadamard's type integral inequalities, Hölder's integral inequality, and詹森（Jensen）的离散和积分不平等，就较高衍生品及其规范而言，调查了杨体积分不平等的几种改进的几种应用，并通过Pólya的类型积分不等式进一步完善了Young的积分不平等。
In the paper, the authors review several refinements of Young's integral inequality via several mean value theorems, such as Lagrange's and Taylor's mean value theorems of Lagrange's and Cauchy's type remainders, and via several fundamental inequalities, such as Čebyšev's integral inequality, Hermite--Hadamard's type integral inequalities, Hölder's integral inequality, and Jensen's discrete and integral inequalities, in terms of higher order derivatives and their norms, survey several applications of several refinements of Young's integral inequality, and further refine Young's integral inequality via Pólya's type integral inequalities.
