Some More Results on a Generalized Parametric R-Norm Information Measure of Type α

Satish Kumar This email address is being protected from spambots. You need JavaScript enabled to view it.¹, Arun Choudhary² and Rajesh Kumar³

¹Department of Mathematics, College of Natural Sciences, Arba-Minch University, Arba-Minch, Ethiopia
²Department of Mathematics, Geeta Institute of Management & Technology, Kanipla-136131, Kurukshetra, Haryana, India
³Department of Mathematics, Hindu College, University of Delhi, Delhi-7, India

REFERENCES

1. [1] Boekee, D. E. and Van Der Lubbe, J. C. A., “The R-Norm Information Measure,” Information and Control, Vol. 45, pp. 136 155 (1980). doi: 10.1016/ S0019-9958(80)90292-2
2. [2] Shannon, C. E., “A Mathematical Theory of Communication,” Bell System Tech. J., Vol. 27, pp. 379 423, 623 656 (1948). doi: 10.1002/j.1538-7305.1948. tb01338.x
3. [3] Renyi, A., “On Measure of Entropy and Information,” Proc. 4th Berkeley Symp. Maths. Stat. Prob., Vol. 1, pp. 547 561 (1961).
4. [4] Havrda, J. F. and Charvat, F., “Qualification Method of Classification Process, the Concept of Structural - Entropy,” Kybernetika, Vol. 3, pp. 30 35 (1967).
5. [5] Daroczy, Z., “Generalized Information Function,” Information and Control, Vol. 16, pp. 36 51 (1970). doi: 10.1016/S0019-9958(70)80040-7
6. [6] Hooda, D. S. and Ram, A., “Characterization of the Generalized R-Norm Entropy,” Accepted for Publication in Caribbean Journal of Mathematical and Computer Science, Vol. 8 (1998).
7. [7] Arimoto, S., “Information Theoretical Consideration on Estimation Problems,” Information and Control, Vol. 19, pp. 181 199 (1971). doi: 10.1016/S0019- 9958(71)90065-9
8. [8] Feinstein, A., Foundation of Information Theory, McGraw Hill, New York (1956).
9. [9] Campbell, L. L., “A Coding Theorem and Renyi’s Entropy,” Information and Control, Vol. 8, pp. 423 429 (1965). doi: 10.1016/S0019-9958(65)90332-3
10. [10] Kieffer, J. C., “Variable Lengths Source Coding with a Cost Depending Only on the Codeword Length,” Information and Control, Vol. 41, pp. 136 146 (1979). doi: 10.1016/S0019-9958(79)90521-7
11. [11] Jelinek, F., “Buffer Overflow in Variable Length Coding of Fixed Rate Sources,” IEEE Transactions on Infformation Theory, Vol. 3, pp. 490 501 (1980). doi: 10.1109/TIT.1968.1054147
12. [12] Hooda, D. S. and Bhaker, U. S., “A Generalized ‘Useful’ Information Measure and Coding Theorems,” Soochow J. Math., Vol. 23, pp. 53 62 (1997). doi: 10.1016/0020-0255(81)90037-2
13. [13] Aczel, J. and Daroczy, Z., “Uber Verallegemeineste Quasiliniare Mittelveste Die Mit Grewinebts Functionen Gebildet SIND,” Pub. Math. Debrecan, Vol. 10, pp. 171 190 (1963).
14. [14] Kapur, J. N., “Generalized Entropy of Order and Type ,” Maths. Seminar, Delhi, Vol. 4, pp. 78 94 (1967).
15. [15] Gurdial and Pessoa, F., “On Useful Information of Order ,” J. Comb. Information and Syst. Sci., Vol. 2, pp. 30 35 (1977).
16. [16] Khan, A. B., Bhat, B. A. and Pirzada, S., “Some Results on a Generalized Useful Information Measure,” Journal of Inequalities in Pure and Applied Mathematics, Vol. 6, No. 4, Art. 117 (2005).
17. [17] Longo, G., “A Noiseless Coding Theorem for Sources Having Utilities,” SIAM J. Appl. Math., Vol. 30, pp. 739 748 (1976). doi: 10.1137/0130067
18. [18] Parkash, Om and Sharma, P. K., “Noiseless Coding Theorems Corresponding to Fuzzy Entropies,” Southeast Asian Bulletin of Mathematics, Vol. 27, pp. 1073 1080 (2004). doi: 10.1109/FUZZ.2001.1007276
19. [19] Singh, R. P., Kumar, R. and Tuteja, R. K., “Application of Hölder’s Inequality in Information Theory,” Information Sciences, Vol. 152, pp. 145 154 (2003). doi: 10.1016/S0020-0255(02)00300-6
20. [20] Kumar, S. and Choudhary, A., “Some Coding Theorems on Generalized Havrda-Charvat and Tsallis’s Entropy,” Tamkang Journal of Mathematics, Vol. 43, pp. 437 444 (2012). doi: 10.5556/j.tkjm.43.2012.437-444
21. [21] Mitter, J. and Mathur, Y. D., “Comparison of Entropies of Power Distribution,” ZAMM, Vol. 52, pp. 239 240 (1972). doi: 10.1002/zamm.19720520406
22. [22] Shisha, O., Inequalities, Academic Press, New York (1967).
23. [23] Beckenbach, E. F. and Bellman, R., Inequalities, Springer, Berlin (1961). doi: 10.1007/978-3-642-64971-4