Univariate Integral Inequalities Based on Sobolev Representations

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


Here we present very general univariate tight integral inequalities of Cheby-shev– Grüss, Ostrowski types for comparison of integral means and information theory. These are based on the well-known Sobolev integral representations of a function. The inequalities engage ordinary and weak derivatives of the involved functions. Applications are given. On the way to prove the main results we derive important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. The results are explained thoroughly. This chapter relies on [4].


Generalize Entropy Representation Formula Integral Inequality Hellinger Distance Weak 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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