Survey On Classical Inequalities by Themistocles RassiasSurvey On Classical Inequalities by Themistocles Rassias

Survey On Classical Inequalities

byThemistocles Rassias

Paperback | October 28, 2012

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Survey on Classical Inequalities provides a study of some of the well known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shannon's and related inequalities, generalized Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp -norm inequalities in convolutions, inequalities for polynomial zeros as well as applications in a number of problems of pure and applied mathematics. It is my pleasure to express my appreciation to the distinguished mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staff of Kluwer Academic Publishers. June 2000 Themistocles M. Rassias Vll LYAPUNOV INEQUALITIES AND THEIR APPLICATIONS RICHARD C. BROWN Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA. email DON B. HINTON Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA. email address: Abstract. For nearly 50 years Lyapunov inequalities have been an important tool in the study of differential equations. In this survey, building on an excellent 1991 historical survey by Cheng, we sketch some new developments in the theory of Lyapunov inequalities and present some recent disconjugacy results relating to second and higher order differential equations as well as Hamiltonian systems. 1. Introduction Lyapunov's inequality has proved useful in the study of spectral properties of ordinary differential equations. Typical applications include bounds for eigenvalues, stability criteria for periodic differential equations, and estimates for intervals of disconjugacy.
Title:Survey On Classical InequalitiesFormat:PaperbackDimensions:237 pagesPublished:October 28, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401058687

ISBN - 13:9789401058681


Table of Contents

Preface. Lyapunov Inequalities and their Applications; R.C. Brown, D.B. Hinton. Classical Hardy's and Carleman's Inequalities and Mixed Means; A. Cizmesija, J. Pecaric. Operator Inequalities Associated with Jensen's Inequality; F. Hansen. Hardy-Littlewood-type Inequalities and their Factorized Enhancement; L. Leindler. Shannon's and Related Inequalities in Information Theory; M. Matic, C.E.M. Pearce, J. Pecaric. Inequalities for Polynomial Zeros; G.V. Milovanovic, T.M. Rassias. On Generalized Shannon Functional Inequality and its Applications; P.K. Sahoo. Weighted Lp-norm Inequalities in Convolutions; S. Saitoh. Index. List of Tables: Table 1. Sample Table. Table 2. Sample table caption. Table 3. Sample Table. Table 4. Sample table caption.