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Summary:
Entropy of type $(\alpha, \beta)$ is characterized in this paper by an axiomatic approach. It includes, in particular, a measure of type $\beta$ earlier studied by many authors. This measure has been studied also by Sharma and Taneja by generalizing a functional equation earlier considered by Chaundy and McLeod. Some properties of this measure are also studied in this paper.
References:
[1] T. W. Chaundy J. B. McLeod: On a functional equation. Proc. Edin. Math. Soc. Edin. Math. Notes 43 (1960), 6-7. MR 0151748
[2] Z. Daróczy: Generalized Information Functions. Information and Control 16 (1970), 36-51. DOI 10.1016/S0019-9958(70)80040-7 | MR 0272528
[3] J. Havrda F. Charvát: Quantification Method of Classification Processes. Concept of Structural a-Entropy. Kybernetika 3 (1967), 30-35. MR 0209067
[4] C. E. Channon: A mathematical theory of communication. B.S.T.J. 27 (1948), 379 - 423, 623-656. MR 0026286
[5] B. D. Sharma I. J. Taneja: Functional Measures in Information Theory. Funkcialaj Ekvacioj 17(1974), 181-191. MR 0379033
[6] B. D. Sharma I. J. Taneja: Entropy of type ($\alpha$, $\beta$) and other generalized measures in information theory. Metrika 22 (1975), 205-215. DOI 10.1007/BF01899728 | MR 0398670
[7] B. D. Sharma I. J. Taneja: Three Generalized-Additive Measures of Entropy. E. I. K. (Germany), vol. 13 (1977), 271-285. MR 0530208
[8] I. J. Taneja: A Joint Characterization of Shannon's Entropy and Entropy of Type $\beta$ through a Functional Equation. Journal of Mathematical Sciences (India) 10 (1975), 69-74. MR 0539497
[9] I. J. Taneja: On the Branching Property of Entropy. To appear in Annales Polonici Mathematici (Poland), Vol. XXXV, 1978. MR 0499877
[10] I. J. Taneja: A Functional Equation of Type ($\alpha$, $\beta$) in Information Theory. Communicated.
[11] I. Vajda: Axioms for a-Entropy of a Generalized Probability Scheme. Kybernetika 2 (1968), 105-112. MR 0233626 | Zbl 0193.48201
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