On the equation associated with bounded paraconcave entropies

• Autorzy: Dudek Z.
• Języki publikacji: EN

Abstrakty

EN

A paraconcave entropy function [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(sum j f(pj)) = sum j g(pj)i, that describes equivalence between two representations of a paraconcave entropy function with concave functions f and g satisfying the condition for a bounded entropy. With the use of E-transforms of the functions f and g we reduce the problem of solvability of the equation to the problem ofinjectivity of a certain nonlinear operator denned on the set of concave homeomorphisms of the interval [0,1] onto itself. Additionally, we prove some facts about concavity of the E-transform f.

Słowa kluczowe

EN

real functions; functional equations; entropy function

PL

funkcje rzeczywiste; funkcje entropowe; równania funkcyjne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 2
• Strony: 401--411
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Dudek Z.

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

Bibliografia

• [1] J. Aczel and Z. Daroczy, On Measures of Information and Their Characterizations, Academic Press, New York, San Francisco, London 1975.
• [2] M. Behara and Z. Dudek, On paraconcave entropy functions, Information Sciences (INS) 64 (1,2), 1992.
• [3] Z. Daroczy, Generalized information functions, Information and Control 16, 1, (1970) 36-51.
• [4] Z. Dudek, On the functional equation associated with unbounded complete paraconcave entropies, Demonstratio Math. 34 (2001), 641-650.
• [5] B. Forte, Derivation of a class of entropies including those of degree β*, Information and Control 28 (1975) , 335-351.
• [6] L. Losonczi, A characterization of entropies of degree α, Metrika (1981), 237-244.
• [7] H. L. Royden, Real Analysis, Macmillan, New York, 1988.