On the functional equation associated with unbounded complete paraconcave entropies

• Autorzy: Dudek Z.
• Języki publikacji: EN

Abstrakty

EN

A paraconcave entropy function, as defined in [2], is represented by a pair of two real functions of a real variable satisfying certain natural conditions. The subject of this paper is the functional equation, L [ sigma j f(pj)]= sigma j g(pj), that describes equivalence between two representations of a paraconcave entropy function with / and g satisfying the condition for unbounded entropy. We show that the above equation has a unique solution up to a multiplicative constant in the class of unbounded and complete paraconcave entropy functions. This is a generalization of the result [4] proven already for incomplete paraconcave entropy functions. This is done by invoking a special version of theCauchy classical functional equation [1]. Additionally, we prove some theorems about ranges of the sums sigma j f(pj) that occur in the investigated equation.

Słowa kluczowe

EN

functional equations; paraconcave entropy

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 3
• Strony: 641--650
• Opis fizyczny: Biblogr. 7 poz.

Twórcy

autor

Dudek Z.

• Faculty of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1 00-661 Warsaw, Poland

Bibliografia

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• [2] M. Behara, Z. Dudek, On concave entropies of discrete systems, Statistical Papers 31, (1990) 77-80.
• [3] M. Behara, Z. Dudek, On paraconcave entropy functions, Information Sciences (INS) 64(1,2), (1992).
• [4] Z. Dudek, On a certain functional equation associated with the paraconcave entropies, Demonstratio Math. 25 (1992), 809-815.
• [5] L. Losonczi, A characterization of entropies of degree a, Metrika, (1981), 237-244.
• [6] C. T. Ng, On the functional equation (…), Ann. Polon. Math., 27 (1973), 329-336.
• [7] H. L. Royden, Real Analysis, Macmillan, New York, 1988.