Classical and New Inequalities in Analysis / Edition 1

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

Overview

One service mathematic;., has Jcndcml the 'Et moi, .. si j'avait su comment CD revcnir, human race. It has put COIDDlOJI SCIISC back je n'y scrais point allC.' whc: rc it belongs, on the topmost shell next Jules Verne to the dusty canister labc1lcd 'dilcardcd nOD- The series is divergent; tbcre(on: we may be sense'. Eric T. Bcll able to do something with it o. Hcavisidc Mathematics is a tool for thought. A highly necessary tooll in a world where both feedbaclt and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other paJts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Product Details

ISBN-13:	9780792320647
Publisher:	Springer Netherlands
Publication date:	12/31/1992
Series:	Mathematics and its Applications , #61
Edition description:	1993
Pages:	740
Product dimensions:	6.14(w) x 9.21(h) x 0.06(d)

Table of Contents

I. Convex functions and Jensen’s inequality.- II. Some recent results involving means.- III. Bernoulli’s inequality.- IV. Cauchy’s and related inequalities.- V. Hölder’s and Minkowski’s inequalities.- VI. Generalized Hölder and Minkowski inequalities.- VII. Connections between general inequalities.- VIII. Some Determinantal and Matrix inequalities.- IX.—ebyšev’s inequality.- X. Grüss’ inequality.- XI. Steffensen’s inequality.- XII. Abel’s and related inequalities.- XIII. Some inequalities for monotone functions.- XIV. Young’s inequality.- XV. Bessel’s inequality.- XVI. Cyclic inequalities.- XVII. Triangle inequalities.- XVIII. Norm inequalities.- XIX. More on norm inequalities.- XX. Gram’s inequality.- XXI. Fejér-Jackson’s inequalities and related results.- XXII. Mathieu’s inequality.- XXIII. Shannon’s inequality.- XXIV. Turán’s inequality from the power sum theory.- XXV. Continued fractions and Padé approximation method.- XXVI. Quasilinearizai ion methods for proving inequalities.- XXVII. The centroid method in inequalities.- XXVIII. Dynamic programming and functional equation approaches to inequalities.- XXIX. Interpolation inequalities.- XXX. Convex Mini max inequalities-equalities.- Name Index.

Editorial Reviews

‘ 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

From the Publisher

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)

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