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 address:dicbrown@bama.ua.edu DON B. HINTON Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA. email address: hinton@novell.math.utk.edu 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.
Erscheinungsdatum: 28.10.2012

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by Themistocles M. Rassias

Springer Science + Business Media BV

Springer Nature

Mathematics and Its Applications -- 517, Dordrecht, Netherlands, 2000

Mathematics and Its Applications, 1st ed. 2000, Dordrecht, 2000

Springer Nature, Dordrecht, 2012

Netherlands, Netherlands

1, 20121206

lg951084

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This volume 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, generalised Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted L p -norm inequalities in convolutions, Heyers-Ulam stability of functional equations in connection with classical inequalities, inequalities for polynomial zeros, as well as applications in a number of problems of pure and applied mathematics.
Audience: This book will be of interest to mathematicians and graduate students whose work involves real functions, functions of a complex variable, functional analysis, approximation theory, numerical analysis, and other subjects of mathematical analysis

Front Matter....Pages i-vii
Lyapunov Inequalities and their Applications....Pages 1-25
Classical Hardy’s and Carleman’s Inequalities and Mixed Means....Pages 27-65
Operator Inequalities Associated with Jensen’s Inequality....Pages 67-98
Hardy-Littlewood-Type Inequalities and their Factorized Enhancement....Pages 99-125
Shannon’s and Related Inequalities in Information Theory....Pages 127-164
Inequalities for Polynomial Zeros....Pages 165-202
On Generalized Shannon Functional Inequality and its Applications....Pages 203-224
Weighted L p -Norm Inequalities in Convolutions....Pages 225-234
Back Matter....Pages 235-237

2013-08-01