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Ostrowski Type Inequalities and Applications in Numerical Integration

  • Sever S. Dragomir
  • Themistocles M. Rassias

Table of contents

  1. Front Matter
    Pages i-xix
  2. Sever S. Dragomir, Themistocles M. Rassias
    Pages 1-63
  3. Pietro Cerone, Sever S. Dragomir
    Pages 141-250
  4. Neil S. Barnett, Pietro Cerone, Sever S. Dragomir
    Pages 285-329
  5. John Roumeliotis
    Pages 373-416
  6. Sever S. Dragomir, Themistocles M. Rassias
    Pages 417-477
  7. Back Matter
    Pages 479-481

About this book

Introduction

It was noted in the preface of the book "Inequalities Involving Functions and Their Integrals and Derivatives", Kluwer Academic Publishers, 1991, by D.S. Mitrinovic, J.E. Pecaric and A.M. Fink; since the writing of the classical book by Hardy, Littlewood and Polya (1934), the subject of differential and integral inequalities has grown by about 800%. Ten years on, we can confidently assert that this growth will increase even more significantly. Twenty pages of Chapter XV in the above mentioned book are devoted to integral inequalities involving functions with bounded derivatives, or, Ostrowski type inequalities. This is now itself a special domain of the Theory of Inequalities with many powerful results and a large number of applications in Numerical Integration, Probability Theory and Statistics, Information Theory and Integral Operator Theory. The main aim of the present book, jointly written by the members of the Vic­ toria University node of RGMIA (Research Group in Mathematical Inequali­ ties and Applications, http: I /rgmia. vu. edu. au) and Th. M. Rassias, is to present a selected number of results on Ostrowski type inequalities. Results for univariate and multivariate real functions and their natural applications in the error analysis of numerical quadrature for both simple and multiple integrals as well as for the Riemann-Stieltjes integral are given.

Keywords

Approximation Numerical integration Operator theory Probability theory approximation theory numerical analysis numerical quadrature statistics

Editors and affiliations

  • Sever S. Dragomir
    • 1
  • Themistocles M. Rassias
    • 2
  1. 1.School of Communications and InformaticsVictoria UniversityMelbourneAustralia
  2. 2.Department of MathematicsNational Technical University of AthensAthensGreece

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-2519-4
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5990-1
  • Online ISBN 978-94-017-2519-4
  • Buy this book on publisher's site