Analytic Inequalities
Published on 20. February 2012
Book
Paperback/Softback
XII, 404 pages
978-3-642-99972-7 (ISBN)
Description
The Theory of Inequalities began its development from the time when C. F. GACSS, A. L. CATCHY and P. L. CEBYSEY, to mention only the most important, laid the theoretical foundation for approximative meth ods. Around the end of the 19th and the beginning of the 20th century, numerous inequalities were proyed, some of which became classic, while most remained as isolated and unconnected results. It is almost generally acknowledged that the classic work "Inequali ties" by G. H. HARDY, J. E. LITTLEWOOD and G. POLYA, which appeared in 1934, transformed the field of inequalities from a collection of isolated formulas into a systematic discipline. The modern Theory of Inequalities, as well as the continuing and growing interest in this field, undoubtedly stem from this work. The second English edition of this book, published in 1952, was unchanged except for three appendices, totalling 10 pages, added at the end of the book. Today inequalities playa significant role in all fields of mathematics, and they present a very active and attractive field of research. J. DIEUDONNE, in his book "Calcullnfinitesimal" (Paris 1968), attri buted special significance to inequalities, adopting the method of exposi tion characterized by "majorer, minorer, approcher". Since 1934 a multitude of papers devoted to inequalities have been published: in some of them new inequalities were discovered, in others classical inequalities ,vere sharpened or extended, various inequalities ,vere linked by finding their common source, while some other papers gave a large number of miscellaneous applications.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1970
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XII, 404 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 23 mm
Weight
633 gr
ISBN-13
978-3-642-99972-7 (9783642999727)
DOI
10.1007/978-3-642-99970-3
Schweitzer Classification
Other editions
Additional editions
Dragoslav S. Mitrinovic | P.M. Vasic
Analytic Inequalities
E-Book
12/2012
Springer
€106.99
Available for download
Dragoslav S. Mitrinovic | P.M. Vasic
Analytic Inequalities
Book
01/1970
1st Edition
Springer
€85.55
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Content
1. Introduction.- 1.1 Real Number System.- 1.2 Complex Number System.- 1.3 Monotone Functions.- 1.4 Convex Functions.- 2. General Inequalities.- 2.1 Fundamental Inequalities.- 2.2 Abel's Inequality.- 2.3 Jordan's Inequality.- 2.4 Bernoulli's Inequality and its Generalizations.- 2.5 ?ebysev's and Related Inequalities.- 2.6 Cauchy's and Related Inequalities.- 2.7 Young's Inequality.- 2.8 Hölder's Inequality.- 2.9 Minkowski's and Related Inequalities.- 2.10 Inequalities of Aczél, Popoviciu, Kurepa and Bellman.- 2.11 Schweitzer's, Diaz-Metcalf's, Rennie's and Related Inequalities.- 2.12 An Inequality of Fan and Todd.- 2.13 Grüss' Inequality.- 2.14 Means.- 2.15 Symmetric Means and Functions.- 2.16 Steffensen's and Related Inequalities.- 2.17 Schur's Inequality.- 2.18 Turán's Inequalities.- 2.19 Benson's Method.- 2.20 Recurrent Inequalities of Redheffer.- 2.21 Cyclic Inequalities.- 2.22 Inequalities Involving Derivatives.- 2.23 Integral Inequalities Involving Derivatives.- 2.24 Inequalities Connected with Majorization of Vectors.- 2.25 Inequalities for Vector Norms.- 2.26 Mills Ratio and Some Related Results.- 2.27 Stirling's Formula.- 3. Particular Inequalities.- 3.1 Inequalities Involving Functions of Discrete Variables.- 3.2 Inequalities Involving Algebraic Functions.- 3.3 Inequalities Involving Polynomials.- 3.4 Inequalities Involving Trigonometric Functions.- 3.5 Inequalities Involving Trigonometric Polynomials.- 3.6 Inequalities Involving Exponential, Logarithmic and Gamma Functions.- 3.7 Integral Inequalities.- 3.8 Inequalities in the Complex Domain.- 3.9 Miscellaneous Inequalities.- Name Index.