Geodesic
On axiomatic characterization of entropy of type $(\alpha,\beta)$
Applications of Mathematics, Tome 22 (1977) no. 6, pp. 409-417

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

DOI MR   Zbl

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.
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.
DOI : 10.21136/AM.1977.103717
Classification : 28D20, 94A15, 94A17 
Taneja, Inder Jeet. On axiomatic characterization of entropy of type $(\alpha,\beta)$. Applications of Mathematics, Tome 22 (1977) no. 6, pp. 409-417. doi: 10.21136/AM.1977.103717
@article{10_21136_AM_1977_103717,
     author = {Taneja, Inder Jeet},
     title = {On axiomatic characterization of entropy of type $(\alpha,\beta)$},
     journal = {Applications of Mathematics},
     pages = {409--417},
     year = {1977},
     volume = {22},
     number = {6},
     doi = {10.21136/AM.1977.103717},
     mrnumber = {0469524},
     zbl = {0385.28013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1977.103717/}
}
TY  - JOUR
AU  - Taneja, Inder Jeet
TI  - On axiomatic characterization of entropy of type $(\alpha,\beta)$
JO  - Applications of Mathematics
PY  - 1977
SP  - 409
EP  - 417
VL  - 22
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1977.103717/
DO  - 10.21136/AM.1977.103717
LA  - en
ID  - 10_21136_AM_1977_103717
ER  - 
%0 Journal Article
%A Taneja, Inder Jeet
%T On axiomatic characterization of entropy of type $(\alpha,\beta)$
%J Applications of Mathematics
%D 1977
%P 409-417
%V 22
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1977.103717/
%R 10.21136/AM.1977.103717
%G en
%F 10_21136_AM_1977_103717

[1] T. W. Chaundy J. B. McLeod: On a functional equation. Proc. Edin. Math. Soc. Edin. Math. Notes 43 (1960), 6-7. | MR

[2] Z. Daróczy: Generalized Information Functions. Information and Control 16 (1970), 36-51. | DOI | MR

[3] J. Havrda F. Charvát: Quantification Method of Classification Processes. Concept of Structural a-Entropy. Kybernetika 3 (1967), 30-35. | MR

[4] C. E. Channon: A mathematical theory of communication. B.S.T.J. 27 (1948), 379 - 423, 623-656. | MR

[5] B. D. Sharma I. J. Taneja: Functional Measures in Information Theory. Funkcialaj Ekvacioj 17(1974), 181-191. | MR

[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 | MR

[7] B. D. Sharma I. J. Taneja: Three Generalized-Additive Measures of Entropy. E. I. K. (Germany), vol. 13 (1977), 271-285. | MR

[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

[9] I. J. Taneja: On the Branching Property of Entropy. To appear in Annales Polonici Mathematici (Poland), Vol. XXXV, 1978. | MR

[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 | Zbl

Cité par Sources :