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Survey on Classical Inequalities pp 203–224Cite as

On Generalized Shannon Functional Inequality and its Applications

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

Abstract

In all measures of information, the entropy f of a single event with probability p plays a fundamental role. The entropy function f, which is also known as the self information satisfies axioms of nonnegativity, additivity and maximality, that is

$$ \begin{gathered} \left( a \right)\;f\left( p \right) \geqslant 0,\quad p \in \left] {0,1} \right[, \hfill \\ \left( b \right)f\left( {pq} \right) = f\left( p \right) + f\left( q \right),\quad p,q \in \left] {0,1} \right[, \hfill \\ \left( c \right)f\left( {\tfrac{1}{2}} \right) = 1. \hfill \\ \end{gathered} $$

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Authors and Affiliations

  1. Department of Mathematics, University of Louisville, Louisville, Kentucky, 40292, USA

    Prasanna K. Sahoo

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  1. Prasanna K. Sahoo
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© 2000 Springer Science+Business Media Dordrecht

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Sahoo, P.K. (2000). On Generalized Shannon Functional Inequality and its Applications. In: Survey on Classical Inequalities. Mathematics and Its Applications, vol 517. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4339-4_7

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  • DOI: https://doi.org/10.1007/978-94-011-4339-4_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5868-1

  • Online ISBN: 978-94-011-4339-4

  • eBook Packages: Springer Book Archive

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