A Functional Generalization of Trapezoid Inequality

被引：0
|
作者：
Dragomir S.S. [1 ,2 ]
机构：
[1] Mathematics, College of Engineering & Science, Victoria University, PO Box 14428, Melbourne City, 8001, MC
[2] School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg
来源：
Vietnam Journal of Mathematics | 2015年 / 43卷 / 4期
关键词：
Absolutely continuous functions; Convex functions; Integral inequalities; Jensen’s inequality; Lebesgue norms; Trapezoid inequality;
D O I：
10.1007/s10013-015-0142-2
中图分类号：
学科分类号：
摘要：
We show in this paper amongst others that, if (Formula presented.) is absolutely continuous on [a,b] and (Formula presented.) is convex (concave) on (Formula presented.) then (Formula presented.) (Formula presented.) for any x∈[a,b]. Natural applications for power and exponential functions are provided as well. Bounds for the Lebesgue p-norms are also given. © 2015, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.
引用
收藏
页码：663 / 675
页数：12
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