Classical and New Inequalities in Analysis / Edition 1

Classical and New Inequalities in Analysis / Edition 1

by Dragoslav S. Mitrinovic, J. Pecaric, A.M Fink
     
 

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

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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.

Product Details

ISBN-13:
9780792320647
Publisher:
Springer Netherlands
Publication date:
12/31/1992
Series:
Mathematics and its Applications Series, #61
Edition description:
1993
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. IConvex functions and Jensen's inequality1
Ch. IISome recent results involving means21
Ch. IIIBernoulli's inequality65
Ch. IVCauchy's and related inequalities83
Ch. VHolder's and Minkowski's inequalities99
Ch. VIGeneralized Holder and Minkowski inequalities135
Ch. VIIConnections between general inequalities191
Ch. VIIISome Determinantal and Matrix inequalities211
Ch. IXCebysev's inequality239
Ch. XGruss' inequality295
Ch. XISteffensen's inequality311
Ch. XIIAbel's and related inequalities333
Ch. XIIISome inequalities for monotone functions365
Ch. XIVYoung's inequality379
Ch. XVBessel's inequality391
Ch. XVICyclic inequalities407
Ch. XVIITriangle inequalities473
Ch. XVIIINorm inequalities515
Ch. XIXMore on norm inequalities559
Ch. XXGram's inequality595
Ch. XXIFejer-Jackson's inequalities and related results611
Ch. XXIIMathieu's inequality629
Ch. XXIIIShannon's inequality635
Ch. XXIVTuran's inequality from the power sum theory651
Ch. XXVContinued fractions and Pade approximation method661
Ch. XXVIQuasilinearization methods for proving inequalities669
Ch. XXVIIThe centroid method in inequalities681
Ch. XXVIIIDynamic programming and functional equation approaches to inequalities697
Ch. XXIXInterpolation inequalities709
Ch. XXXConvex Mini max inequalities-equalities721
Name Index725

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