Regular Article
On a Class of Functional Equations in Distribution

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Abstract

In this article, we present the most general solution of the functional equationsf(xy) + f((1  x)(1  y)) = f(x(1  y)) + f(y(1  x)) andf(xy) + f(x(1  y)) + f(y(1  x)) + f((1  x)(1  y)) = f(x) + f(1  x) + f(y) + f(1  y) in the domain of distributions; and show that for regular distributions the solutions are the same as the classical solutions. These functional equations arise in connection with the characterization of sum form information measures.

Keywords

information measures
functional equation
distributions
linear operators

Cited by (0)

Submitted by William, F. Ames

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Partially supported by ORC Grant, UH-Downtown. E-mail address:[email protected].

Partially supported by ORC Grant, UH-Downtown.