Inequalities: Theory of Majorization and Its Applications, Second Edition
Inequalities: Theory of Majorization and Its Applications, Second Edition
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DOI：
10.1007/978-0-387-68276-1
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发表时间：
2011-01-01
期刊：
影响因子：
--
通讯作者：
Arnold, Barry C.
中科院分区：
文献类型：
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作者：
Marshall, Albert W.;Olkin, Ingram;Arnold, Barry C.
虽然不等式在几乎所有的数学分支中都扮演着重要的角色，但它们通常是通过特殊的方法获得的，而不是作为一些基本的“不等式理论”的结果。对于某些类型的不等式，控制的概念导致这样一个理论，有时是非常有用和强大的推导不等式。此外，通过优控制方法推导不等式通常对于提供更深入的理解和提出自然的推广都非常有帮助。随着20世纪60年代的发展，我们越来越意识到这些事实。我们在1967-1968年访问剑桥大学时举办的一系列研讨会加强了我们的意识。因为与优化相关的思想值得更好地了解，我们决定在1970年之前就这个主题写一本小专著--一本可能有100页之多--这就是本书的起源。优化的思想是几个更一般的概念的特殊情况，但是本书中提到这些概括只是为了它们提供的观点。我们将自己限制在主要化的各个方面，部分是因为我们想强调它的重要性，部分是因为它的简单性吸引了我们。然而，为了使
Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying “theory of inequalities.” For certain kinds of inequalities, the notion of majorization leads to such a theory that is sometimes extremely useful and powerful for deriving inequalities. Moreover, the derivation of an inequality by methods of majorization is often very helpful both for providing a deeper understanding and for suggesting natural generalizations. As the 1960s progressed, we became more and more aware of these facts. Our awareness was reinforced by a series of seminars we gave while visiting the University of Cambridge in 1967–1968. Because the ideas associated with majorization deserve to be better known, we decided by 1970 to write a little monograph on the subject—one that might have as many as 100 pages—and that was the genesis of this book.The idea of majorization is a special case of several more general notions, but these generalizations are mentioned in this book only for the perspective they provide. We have limited ourselves to various aspects of majorization partly because we want to emphasize its importance and partly because its simplicity appeals to us. However, to make the