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Survey on Classical Inequalities

  • Themistocles M. Rassias

Part of the Mathematics and Its Applications book series (MAIA, volume 517)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Richard C. Brown, Don B. Hinton
    Pages 1-25
  3. Aleksandra Čižmešija, Josip Pečarić
    Pages 27-65
  4. M. Matić, C. E. M. Pearce, J. Pečarić
    Pages 127-164
  5. Gradimir V. Milovanović, Themistocles M. Rassias
    Pages 165-202
  6. Saburou Saitoh
    Pages 225-234
  7. Back Matter
    Pages 235-237

About this book

Introduction

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.

Keywords

Jensen's inequality convolution functional analysis functional equation

Authors and affiliations

  • Themistocles M. Rassias
    • 1
  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece

Bibliographic information