SciELO - Scientific Electronic Library Online

 
vol.35 issue4Totally magic cordial labeling of mPn and mKnEnergy of strongly connected digraphs whose underlying graph is a cycle author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • On index processCited by Google
  • Have no similar articlesSimilars in SciELO
  • On index processSimilars in Google

Share


Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.4 Antofagasta Dec. 2016

http://dx.doi.org/10.4067/S0716-09172016000400002 

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

 

G. Farid

Atiq Ur Rehman 

COMSATS Institute of Information Technology, Pakistan

J. Pecaric 

University Of Zagreb, Croatia 


ABSTRACT

In this paper, we give an order relation between J-divergence and generalized K-divergence. By using this order relation we give generalizations ofthe 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.

Subjclass [2000] : 94A17, 26B25

Keywords : Convexfunctions, K-divergence, J-divergence, log-convexity, Cauchy means, exponentially convex functions.


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).         [ Links ]

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

[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).         [ Links ]

[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).         [ Links ]

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

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

[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).         [ Links ]

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

[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).         [ Links ]

[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).         [ Links ]

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

[13]    E. C. Pielou, Ecological diversity, Willy, New York, (1975).         [ Links ]

[14]    C. R. Rao, Diversity and dissimilarity coefficients, Theor. Pop. Bio. 21, pp. 24-43, (1982).         [ Links ]

[15]    C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27, pp. 379-423 and pp. 623-656, (1948).         [ Links ]

[16]    A. Ullah, Entropy, divergence and distance measures with econometric applications, J Stat Plan Inference. 49, pp. 137-162, (1996).         [ Links ]

[17]    N. Wiener, Cybernetics or control and communication in the animal and the machine, 2nd Edition, The MIT Press, (1965).         [ Links ]

G. Farid

COMSATS Institute of Information Technology, Attock Campus,

Pakistan

e-mail : ghlmfarid@ciit-attock.edu.pk

Atiq Ur Rehman

COMSATS Institute of Information Technology, Attock Campus,

Pakistan

e-mail : atiq@mathcity.org

J. Pecaric

Faculty Of Textile Technology Zagreb, University Of Zagreb,

Croatia

e-mailpecaric@mahazu.hazu.hr

Received : May 2015. Accepted : September 2016

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License