On the functional equation associated with unbounded complete paraconcave entropies (Q2757035)
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scientific article; zbMATH DE number 1675690
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the functional equation associated with unbounded complete paraconcave entropies |
scientific article; zbMATH DE number 1675690 |
Statements
6 April 2003
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functional equations
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paraconcave entropy
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On the functional equation associated with unbounded complete paraconcave entropies (English)
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The author finds all solutions \((L,f,g)\) of the following equation NEWLINE\[NEWLINEL\Biggl(\sum_j f(p_j)\Biggr)= \sum_j g(p_j),NEWLINE\]NEWLINE where \(L\) is a continuous bijection on \([0,\infty)\) onto itself, \(f\) and \(g\) are continuous concave functions in \([0,1]\) such that \(f(0)= f(1)= g(0)= g(1)= 0\) and \(\sup_N f({1\over n})= \sup_N g({1\over N})= \infty\).
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