Classical and New Inequalities in Analysis / Edition 1

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Overview

This volume presents a comprehensive compendium of classical and new inequalities as well as some recent extensions to well-known ones.
Variations of inequalities ascribed to Abel, Jensen, Cauchy, Chebyshev, Hölder, Minkowski, Stefferson, Gram, Fejér, Jackson, Hardy, Littlewood, Po'lya, Schwarz, Hadamard and a host of others can be found in this volume. The more than 1200 cited references include many from the last ten years which appear in a book for the first time.
The 30 chapters are all devoted to inequalities associated with a given classical inequality, or give methods for the derivation of new inequalities. Anyone interested in equalities, from student to professional, will find their favorite inequality and much more.

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Editorial Reviews

Booknews
A comprehensive compendium of classical and new inequalities as well as some recent extensions to well-known ones. The 30 chapters are all devoted to inequalities associated with a given classical inequality, or give methods for the derivation of new inequalities. Included are variations of inequalities ascribed to Abel, Jensen, Cauchy, Chebyshev, Holder, Minkowski, Steffensen, Gram, Fejer, Jackson, Hardy, Littlewood, Polya, Schwarz, Hadamard, and a host of others. The more than 1,200 cited references include many from the last ten years which appear in a book for the first time. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From the Publisher
' This is an excellent book that seems to prove that there is no possibility of a last word on equalities. All in all this is a book that everyone working with inequalities should have. '
Mathematical Reviews, 94c
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Product Details

  • ISBN-13: 9780792320647
  • Publisher: Springer Netherlands
  • Publication date: 12/31/1992
  • Series: Mathematics and its Applications Series , #61
  • Edition description: 1993
  • Edition number: 1
  • Pages: 740
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.63 (d)

Table of Contents

Preface
Organization of the Book
Notations
Ch. I Convex functions and Jensen's inequality 1
Ch. II Some recent results involving means 21
Ch. III Bernoulli's inequality 65
Ch. IV Cauchy's and related inequalities 83
Ch. V Holder's and Minkowski's inequalities 99
Ch. VI Generalized Holder and Minkowski inequalities 135
Ch. VII Connections between general inequalities 191
Ch. VIII Some Determinantal and Matrix inequalities 211
Ch. IX Cebysev's inequality 239
Ch. X Gruss' inequality 295
Ch. XI Steffensen's inequality 311
Ch. XII Abel's and related inequalities 333
Ch. XIII Some inequalities for monotone functions 365
Ch. XIV Young's inequality 379
Ch. XV Bessel's inequality 391
Ch. XVI Cyclic inequalities 407
Ch. XVII Triangle inequalities 473
Ch. XVIII Norm inequalities 515
Ch. XIX More on norm inequalities 559
Ch. XX Gram's inequality 595
Ch. XXI Fejer-Jackson's inequalities and related results 611
Ch. XXII Mathieu's inequality 629
Ch. XXIII Shannon's inequality 635
Ch. XXIV Turan's inequality from the power sum theory 651
Ch. XXV Continued fractions and Pade approximation method 661
Ch. XXVI Quasilinearization methods for proving inequalities 669
Ch. XXVII The centroid method in inequalities 681
Ch. XXVIII Dynamic programming and functional equation approaches to inequalities 697
Ch. XXIX Interpolation inequalities 709
Ch. XXX Convex Mini max inequalities-equalities 721
Name Index 725
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