Survey on Classical Inequalities: 517 (Mathematics and Its Applications, 517) - Hardcover

Hardcover

ISBN 10: 079236483X ISBN 13: 9780792364832

Publisher: Springer, 2000

Synopsis

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.

About this title

Synopsis

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, generalized Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp-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. The text should be useful 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.

Edition details

• Publisher: Springer
• Publication date: 2000
• ISBN 10: 079236483X
• ISBN 13: 9780792364832
• Binding: Hardcover
• Language: English
• Number of pages: 244
• Editor: RASSIAS Themistocles