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Multivariate Integral Inequalities Deriving from Sobolev Representations

  • George A. AnastassiouEmail author
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

Here we present very general multivariate tight integral inequalities of Chebyshev–Grüss,Ostrowski types and of comparison of integral means. These rely on the well-known Sobolev integral representation of a function. The inequalities engage ordinary and weak partial derivatives of the involved functions.We give also applications. On the way to prove the main results we obtain important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. The exposed results are thoroughly discussed. This chapter relies on [4].

Keywords

Open Ball Integral Inequality Representation Proof Important Estimate Weak Partial Derivative 
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Copyright information

© George A. Anastassiou 2011

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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