Classical and new inequalities in analysis

by D.S. Mitrinović, J.E. Pečarić, and 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, Holder, Minkowski, Stefferson, Gram, Fejer, 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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[目次]

  • 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. Holder and Minkowski Inequalities. VI. Generalized Holder and Minkowski Inequalities. VII. Connections Between General Inequalities. VIII. Some Determinantal and Matrix Inequalities. IX. Cebysev's Inequality. X. Gruss' 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. Frejer-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 Pade 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.

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この本の情報

書名 Classical and new inequalities in analysis
著作者等 Fink, A. M.
Mitrinović, Dragoslav S.
Pečarić, J. E.
Fink A.M.
Pecaric J.E. (University of Zagreb Croatia)
Mitrinovic Dragoslav S.
シリーズ名 Mathematics and its applications
出版元 Kluwer Academic
刊行年月 c1993
ページ数 xvii, 740 p.
大きさ 25 cm
ISBN 0792320646
NCID BA19214331
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言語 英語
出版国 オランダ
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