Inequalities Based on Sobolev Representations

  • George A. Anastassiou

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

About this book

Introduction

Inequalities based on Sobolev Representations deals exclusively with very general tight integral inequalities of Chebyshev-Grüss, Ostrowski types and of integral means, all of which depend upon the Sobolev integral representations of functions.  Applications illustrate inequalities that engage in ordinary and weak partial derivatives of the involved functions. This book also derives important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations.  The results are examined in all directions and through both univariate and multivariate cases. This book is suitable for researchers, graduate students, and seminars in subareas of mathematical analysis, inequalities, partial differential equations and information theory.

Keywords

Information Theory Integral Inequalities Ostrowski Inequality Sobolev Representations Weak Derivative

Authors and affiliations

  • George A. Anastassiou
    • 1
  1. 1.Dept. Mathematical SciencesUniversity of MemphisMemphisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-0201-5
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-0200-8
  • Online ISBN 978-1-4614-0201-5
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • About this book