On generalization of K-divergence, its order relation with J-divergence and related results

Authors

  • G. Farid COMSATS Institute of Information Technology.
  • Atiq Ur Rehman COMSATS Institute of Information Technology.
  • J. Pecaric University Of Zagreb.

DOI:

https://doi.org/10.4067/S0716-09172016000400002

Keywords:

Convex functions, K-divergence, J-divergence, log-convexity, Cauchy means, exponentially convex functions, funciones convexas, K-divergencia, J-divergencia, convexidad logarítmica, valor medio de Cauchy, funciones exponencialmente convexas.

Abstract

In this paper, we give an order relation between J-divergence and generalized K-divergence. By using this order relation we give generalizations of the results related to an order relation between J-divergence and K-divergence given by J. Burbea and C. R. Rao. Also we construct class of m-exponentially convexfunctions introducing by nonnegative difference of new order relation.

Author Biography

J. Pecaric, University Of Zagreb.

Faculty Of Textile Technology Zagreb.

References

[1] M. Anwar, G. Farid and J. Pecaric, Generalization of K-divergence and related results, J. Math. Ineq., 5(2), pp. 181—191, (2011).

[2] L. Boltzman, Neitere Studien fiber das Warmegleichgewicht unter Gasmolekulen, K. Akad. Wiss. (Wein) Sitzb. 66, 275, (1872).

[3] J. Burbea, and C.R. Rao, Entropy differential metric, distance and divergence measures in probability spaces: A unified approach, J. Multivariate Anal. 12(4), pp. 575—596, (1982).

[4] J. Burbea and C. R. Rao, On convexity of some divergence measure based on entropy functions, IEEE Trans. Inform. Theory 28(3), pp. 489—495, (1982).

[5] R. Clausius, Abhaudlungen fiber die mechanische Wiirmetheorie Friedrich Vieweg, Braunschweig, (1864).

[6] R. G. Gallager, Information theory and reliable communication, Willy, New York, (1968).

[7] S. Hussain, On Jensen’s and related inequalities, PhD thesis, Govt. College University, Lahore, 2009. URL: http://eprints.hec.gov.pk/6348/.

[8] R. C. Lewonton, The apportionment of human diversity, Evol. Biol. 6, pp. 381—398, (1972).

[9] P. C. Mahalanobis, On the generalized distance in statistics, Proc. Natl. Inst. Sci. 2(1), pp. 49—55, (1936).

[10] J. Pecaric and J. Peric, Improvements of the Giaccardi and the Petrovic inequality and related Stolarsky type means, An. Univ. Craiova Ser. Mat. Inform., 39(1), pp. 65-75, (2012).

[11] M. A. Noor, K. I. Noor and M. U. Awan, Geometrically relative convex functions, Appl. Math. Inf. Sci. 8(2), pp. 607—616, (2014).

[12] J. E. Pecaric, F. Proschan and Y. L. Tong, Convex functions, partial orderings and statistical applications, Academic Press, New York, (1992).

Published

2017-03-23

How to Cite

[1]
G. Farid, A. U. Rehman, and J. Pecaric, “On generalization of K-divergence, its order relation with J-divergence and related results”, Proyecciones (Antofagasta, On line), vol. 35, no. 4, pp. 381-393, Mar. 2017.

Issue

Section

Artículos