基本信息

書名:不等式(第2版)

定價：59.00元

售價：39.5元,便宜19.5元,摺扣66

作者:G.Hardy,J.E.Littlewood G.Polya

齣版社：世界圖書齣版公司

齣版日期：2004-04-01

ISBN：9787506266062

字數：

頁碼：324

版次：1

裝幀：平裝

開本：24開

商品重量：0.422kg

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內容提要

It is oftereally difficult to trace the origiof a familiar inequality. It is quite likely to occur first as aauxiliary proposition， oftewithout explicit statement， ia memoir ogeometry or astronomy; it may have beerediscovered， many years later， by half a dozedifferent authors; and no accessible statement of it may be quite plete. We have almost always found， evewith the most famous inequalities， that we have a little new to add. We have done our best to be accurate and have giveall references we can， but we have never undertakesystematic bibliographical research. We follow the mopractice， whea particular inequality is habitually associated with a particular mathematicians name; we speak of the inequalities of Schwarz， HSlder， and Jensen， though all these inequalities cabe traced further back; and we do not enumerate explicitly all the minor additions which are necessary for absolute pleteness. We have received a great deal of assistance from friends. Messrs G. A. Bliss， L. S. Bosanquet， R. Courant， B. Jessen， V. Levin， R. Rado， I. Schur， L. C. Young， and A. Zygmund have all helped us with criticisms or original contributions. Dr Bosanquet， Dr Jessen， and Prof. Zygmund have read tho proofs， and corrected many inaccuracies. Iparticular， Chapter III has beevery largely rewritteas the result of Dr Jessens suggestions. We hope that the book may now be reasonably free from error， ispite of the mass of detail which it contains.
　　本書為英文版。

目錄

CHAPTER Ⅰ INTRODUCTION
1.1 Finite,infinite,and integral inequalities
1.2 Notations
1.3 Positive inequalities
1.4 Homogeneous inequalities
1.5 The axiomatic basis of algebraic inequalities
1.6 Comparable functions
1.7 Selectioof proofs
1.8 Selectioof subjects
CHAPTERⅡ ELEMENTARY MEAN VALUES
2.1 Ordinary means
2.2 Weighted means
2.3 Limiting cases of a
2.4 Cauchys inequality
2.5 The theorem of the arithmetic and geometric means
2.6 Other proofs of the theorem of the means
2.7 Holders inequality and its extensions
2.8 Holders inequality and its extensions cont
2.9 General properties of the means a
2.10 The sums r a
2.11 Minkowskis inequality
2.12 A panioto Minkowskis inequality
2.13 Illustrations and applications of the fundamental inequalities
2.14 Inductive proofs of the fundamental inequalities
2.15 Elementary inequalities connected with Theorem 37
2.16 Elementary proof of Theorem 3
2.17 Tchebyehefs inequality
2.18 Muirheads theorem
2.19 Proof of Muirheads theorem
2.20 Aalternative theorem
2.21 Further theorems osymmetrical means
2.22 The elementary symmetric functions of positive numbers
2.23 A note odefinite forms
2.24 A theorem concerning strictly positive forms Miscellaneous theorems and examples
CHAPTER Ⅲ MEAN VALUES WITH AN ARBITRARY FUNCTION AND THE THEORY OF CONVEX FUNCTIONS
3.1 Definitions
3.2 Equivalent means
3.3 A characteristic property of the means
3.4 Comparability
3.5 Convex functions
3.6 Continuous convex functions
3.7 Aalternative definition
3.8 Equality ithe fundamental inequalities
3.9 Restatements and extensions of Theorem 85
3.10 Twice differentiable convex functions
3.11 Applieations of the properties of twice differentiable convex functions
3.12 Convex functions of several variables
3.13 Generalisations of Holders inequality
3.14 Some theorems concerning monotonic functions
3.15 Sums with aarbitrary function: generalisa. tions of Jensens inequality
3.16 Generalisations of Minkowskis inequality
3.17 Comparisoof sets
3.18 Fur ther general properties of convex functions
3.19 Further properties of continuous convex functions
3.20 Discontinuous convex functions Miscellaneous theorems and examples
……
CHAPTERⅣ VARIOUS APPLICATIONS OF THE CALCULUS
CHAPTERⅤ INFINITE SERIES
CHAPTERⅥ INTEGRALS
CHAPTERⅦ SOME APPLICATIONS OF THE CALCULUS OF VARIATIONS
CHARTERⅧ SOME THEOREMS CONCERNING BILINEAR AND MULTILINEAR FORMS
CHAPTERⅨ HILBERTS INEQUALITY AND ITS ANALOGUES AND EXTENSIONS
CHAPTERⅩ REARRANGEMENTS
APPENDIXⅠ Ostrictly positive forms
APPENDIXⅡ Thorins proof and extensioof Theorem 295
APPENDIXⅢ OHilberts inequality
BIBLIOGRAPHY

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