On the stability of a sum form equation in several variables

• Autorzy: Kocsis I.
• Języki publikacji: EN

Abstrakty

EN

In this note we prove that a sum form functional equation arising in information theory, which holds for all k-dimensional (k > 1 is fixed) complete probability distributions, is stable.

Słowa kluczowe

EN

stability; sum form equation

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr 1
• Strony: 67--92
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Kocsis I.

• Institute of Mathematics and Informatics, University of Debrecen, H-4010, Debrecen P.O. Box 12, Hungary

Bibliografia

• [1] J. Aczel, Z. Daróczy, On Measures o f Information and Their Characterization, Academic Press, New York-San Francisco-London, 1975.
• [2] B. Ebanks, P. Sahoo and W. Sander, Characterizations of information measures, World Scientific, Singapure-New Yersey-London-Hong Kong, 1998.
• [3] G. L. Forti, Hyers-Ulam stability of functional eąuations in several variables, Aequations Math. 50 (1995), 143-190.
• [4] R. Ger, A survey of recent results on stability of functional equations, Proc. of the 4th International Conference of Functional Equations and Inequalities, Pedagogical University of Cracow, 1994, 5-36.
• [5] D. H. Hyers, G. Isac and Th. M. Rassias, Stability of functional equations in several variables, Progress in Nonlinear Differential Equations and their Applications, 34. vol. 27. Birkhauser Verlag, Basel-Boston, 1998.
• [6] L. Losonczi and Gy. Maksa, On some functional equations of the information theory, Acta Math. Acad. Sci. Hungar. 39 (1982), 73-82.
• [7] Gy. Maksa, On the stability of a sum form equation, Results in Mathematics 26 (1994), 342-347.
• [8] Gy. Maksa, The role of boundedness and nonnegativity in characterizing of entropies of degree α, Publ. Math., Debrecen 36 (1989), 179-185.
• [9] F. Radó and J. A. Baker, Pexider’s equation and aggregation of allocations, Aequationes Math. 32 (1987), 227-239.
• [10] L. Szekelyhidi, Ulam’s problem, Hyers’s solution - and to where they led, Functional equations and inequalities, Edited by Th. M. Rassias, Dordrecht: Kluwer Academic Publishers. Math. Appl., Dord. 518 (2000), 259-285.