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On continuous solutions of a functional equation. (English) Zbl 0333.39006


MSC:

39B05 General theory of functional equations and inequalities
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References:

[1] Aczél, J.: Lectures on Functional Equations and their applications. New York-London 1966. · Zbl 0139.09301
[2] –, andZ. Daróczy: Charakterisierung der Entropien positiver Ordnung und der Shannonschen Entropie. Acta Math. Acad. Sci. Hungar14, 95–121, 1963. · Zbl 0138.14904
[3] Chaundy, T.W., andJ.B. McLeod: On a functional equation. Edinburgh Math. Notes43, 7–8, 1960. · Zbl 0100.32703
[4] Daróczy, Z.: Über die Charakterisierung der Shannonschen Entropie. Colloquium on Information Theory Debrecan, 1967.
[5] –: Generalized Information Functions. Information and Control, Vol.16 (1), 36–51, 1970. · Zbl 0205.46901
[6] –: On a measurable solution of a functional equation. Acta Math. Acad. Sci. Hungar22, 11–14, 1971. · Zbl 0236.39008
[7] Havrda, J., andF. Charvát: Quantification method of classification process. The concept of structural {\(\alpha\)}-entropy, Kybernetika3, 30–35, 1967. · Zbl 0178.22401
[8] Kannappan, Pl.: On Shannon’s entropy Directed divergence and Inaccuracy. Z. Wahrscheinlichkeitstheorie Verw. Geb.22, 95–100, 1972. · Zbl 0241.94020
[9] Ng, C.T.: On the measurable solution of the functional equation, 1972. · Zbl 0227.39005
[10] Shannon, C.E.: A mathematical theory of communication. Bell System Tech. J.27, 379–423, 623–656, 1948. · Zbl 1154.94303
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