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On a functional equation connected with Rao's quadratic entropy

Authors: J. K. Chung, B. R. Ebanks, C. T. Ng and P. K. Sahoo
Journal: Proc. Amer. Math. Soc. 120 (1994), 843-848
MSC: Primary 39B22
MathSciNet review: 1180464
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Abstract: We determine the general solution of the functional equation fxy,

$\displaystyle f\left( {\frac{{x + y}} {2}} \right) + f\left( {\frac{{x - y}} {2... ...t( {\frac{x} {2}} \right) + 2f\left( {\frac{y} {2}} \right) + \lambda f(x)f(y),$

/: [- $ f:[ - 1,1] \to {\mathbf{R}}$. This equation was used by Lau in order to characterize Rao's quadratic entropies. The general solution is obtained here as a special case of a more general result for $ f$ mapping a neighborhood of 0 in linear topological space into a field.

References [Enhancements On Off] (What's this?)

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Keywords: Biadditive function, quadratic functional equation, quadratic entropy
Article copyright: © Copyright 1994 American Mathematical Society

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