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＜電子ブック＞
Handbook of Means and Their Inequalities / by P.S. Bullen
(Mathematics and Its Applications ; 560)

版	2nd ed. 2003.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2003
本文言語	英語
大きさ	XXVIII, 538 p : online resource
著者標目	*Bullen, P.S author SpringerLink (Online service)
件　名	LCSH:Functions of real variables LCSH:Sequences (Mathematics) LCSH:Approximation theory LCSH:Statistics  LCSH:Mathematics FREE:Real Functions FREE:Sequences, Series, Summability FREE:Approximations and Expansions FREE:Statistics FREE:Applications of Mathematics
一般注記	I Introduction -- II The Arithmetic, Geometric and Harmonic Means -- III The Power Means -- IV Quasi-Arithmetic Means -- V Symmetric Polynomial Means -- VI Other Topics -- Books -- Papers -- Name Index There seems to be two types of books on inequalities. On the one hand there are treatises that attempt to cover all or most aspects of the subject, and where an attempt is made to give all results in their best possible form, together with either a full proof or a sketch of the proof together with references to where a full proof can be found. Such books, aimed at the professional pure and applied mathematician, are rare. The first such, that brought some order to this untidy field, is the classical "Inequalities" of Hardy, Littlewood & P6lya, published in 1934. Important as this outstanding work was and still is, it made no attempt at completeness; rather it consisted of the total knowledge of three front rank mathematicians in a field in which each had made fundamental contributions. Extensive as this combined knowledge was there were inevitably certain lacunre; some important results, such as Steffensen's inequality, were not mentioned at all; the works of certain schools of mathematicians were omitted, and many important ideas were not developed, appearing as exercises at the ends of chapters. The later book "Inequalities" by Beckenbach & Bellman, published in 1961, repairs many of these omissions. However this last book is far from a complete coverage of the field, either in depth or scope HTTP:URL=https://doi.org/10.1007/978-94-017-0399-4

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