Classical and New Inequalities in Analysis

ISBN-13: 9780792320647 / Angielski / Twarda / 1992 / 740 str.

Dragoslav S. Mitrinovic; J. E. Pecaric; A. M. Fink

Opis

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.

Recenzje

` 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

Spis treści

Preface. Organization of the Book. Notations. 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 and Minkowski Inequalities. VI. Generalized Hölder and Minkowski Inequalities. VII. Connections Between General Inequalities. VIII. Some Determinantal and Matrix Inequalities. IX. Cebysev'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 Inequations. XVII. The Centroid Method in Inequalities. XVII. Triangle Inequalities. XVIII. Norm Inequalities. XIX. More on Norm Inequalities. XX. Gram's Inequality. XXI. Frejér-Jackson's Inequalities and Related Results. XXII. Mathieu's Inequality. XXIII. Shannon's Inequality. XXIV. Turan's Inequality from the Power Sum Theory. XXV. Continued Fractions and Padé Approximation Method. XXVI. Quasilinearization Methods for Proving Inequalities. XXVIII. Dynamic Programming and Functional Equation Approaches to Inequalities. XXIX. Interpolation Inequalities. XXX. Minimax Inequalities. Name Index.