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Year 2019, Volume: 2 Issue: 3, 109 - 123, 01.09.2019

Silvestru Sever Dragomir

https://doi.org/10.33205/cma.562166
Cited By: 3

Abstract

References

  • [1] P. Cerone and S. S. Dragomir, Approximation of the integral mean divergence and f-divergence via mean results. Math. Comput. Modelling 42 (2005), no. 1-2, 207–219.
  • [2] P. Cerone, S. S. Dragomir and F. Österreicher, Bounds on extended f-divergences for a variety of classes, Kybernetika (Prague) 40 (2004), no. 6, 745–756. Preprint, RGMIA Res. Rep. Coll. 6(2003), No.1, Article 5. [ONLINE: http://rgmia.vu.edu.au/v6n1.html].
  • [3] I. Csiszár, Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten. (German) Magyar Tud. Akad. Mat. Kutató Int. Közl. 8 (1963) 85–108.
  • [4] S. S. Dragomir, Some inequalities for (m;M)-convex mappings and applications for the Csiszár $\Phi$-divergence in information theory. Math. J. Ibaraki Univ. 33 (2001), 35–50.
  • [5] S. S. Dragomir, Some inequalities for two Csiszár divergences and applications. Mat. Bilten No. 25 (2001), 73–90.
  • [6] S. S. Dragomir, An upper bound for the Csiszár f-divergence in terms of the variational distance and applications. Panamer. Math. J. 12 (2002), no. 4, 43–54.
  • [7] S. S. Dragomir, Upper and lower bounds for Csiszár f-divergence in terms of Hellinger discrimination and applications. Nonlinear Anal. Forum 7 (2002), no. 1, 1–13
  • [8] S. S. Dragomir, Bounds for f-divergences under likelihood ratio constraints. Appl. Math. 48 (2003), no. 3, 205–223.
  • [9] S. S. Dragomir, New inequalities for Csiszár divergence and applications. Acta Math. Vietnam. 28 (2003), no. 2, 123–134.
  • [10] S. S. Dragomir, A generalized f-divergence for probability vectors and applications. Panamer. Math. J. 13 (2003), no. 4, 61–69.
  • [11] S. S. Dragomir, Some inequalities for the Csiszár '-divergence when ' is an L-Lipschitzian function and applications. Ital. J. Pure Appl. Math. No. 15 (2004), 57–76.
  • [12] S. S. Dragomir, A converse inequality for the Csiszár $\Phi$-divergence. Tamsui Oxf. J. Math. Sci. 20 (2004), no. 1, 35–53.
  • [13] S. S. Dragomir, Some general divergence measures for probability distributions. Acta Math. Hungar. 109 (2005), no. 4, 331–345.
  • [14] S. S. Dragomir, A refinement of Jensen’s inequality with applications for f-divergence measures. Taiwanese J. Math. 14 (2010), no. 1, 153–164.
  • [15] S. S. Dragomir, A generalization of f-divergence measure to convex functions defined on linear spaces. Commun. Math. Anal. 15 (2013), no. 2, 1–14.
  • [16] H. Jeffreys, Theory of Probability, Oxford University Press, 1948, 2nd ed.
  • [17] F. Liese and I. Vajda, Convex Statistical Distances, Teubuer-Texte zur Mathematik, Band 95, Leipzig, 1987.

Inequalities for Synchronous Functions and Applications

Year 2019, Volume: 2 Issue: 3, 109 - 123, 01.09.2019

Silvestru Sever Dragomir

https://doi.org/10.33205/cma.562166
Cited By: 3

Abstract

Some inequalities for synchronous functions that are a mixture between Cebyšev’s and Jensen's inequality are provided. Applications for $f$ -divergence measure and some particular instances including Kullback-Leibler divergence, Jeffreys divergence and $\chi ^{2}$-divergence are also given.

Keywords

Synchronous Functions Lipschitzian functions Jensen's inequality $f$-divergence measure Kullback-Leibler divergence Jeffreys divergence measure

References

  • [1] P. Cerone and S. S. Dragomir, Approximation of the integral mean divergence and f-divergence via mean results. Math. Comput. Modelling 42 (2005), no. 1-2, 207–219.
  • [2] P. Cerone, S. S. Dragomir and F. Österreicher, Bounds on extended f-divergences for a variety of classes, Kybernetika (Prague) 40 (2004), no. 6, 745–756. Preprint, RGMIA Res. Rep. Coll. 6(2003), No.1, Article 5. [ONLINE: http://rgmia.vu.edu.au/v6n1.html].
  • [3] I. Csiszár, Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten. (German) Magyar Tud. Akad. Mat. Kutató Int. Közl. 8 (1963) 85–108.
  • [4] S. S. Dragomir, Some inequalities for (m;M)-convex mappings and applications for the Csiszár $\Phi$-divergence in information theory. Math. J. Ibaraki Univ. 33 (2001), 35–50.
  • [5] S. S. Dragomir, Some inequalities for two Csiszár divergences and applications. Mat. Bilten No. 25 (2001), 73–90.
  • [6] S. S. Dragomir, An upper bound for the Csiszár f-divergence in terms of the variational distance and applications. Panamer. Math. J. 12 (2002), no. 4, 43–54.
  • [7] S. S. Dragomir, Upper and lower bounds for Csiszár f-divergence in terms of Hellinger discrimination and applications. Nonlinear Anal. Forum 7 (2002), no. 1, 1–13
  • [8] S. S. Dragomir, Bounds for f-divergences under likelihood ratio constraints. Appl. Math. 48 (2003), no. 3, 205–223.
  • [9] S. S. Dragomir, New inequalities for Csiszár divergence and applications. Acta Math. Vietnam. 28 (2003), no. 2, 123–134.
  • [10] S. S. Dragomir, A generalized f-divergence for probability vectors and applications. Panamer. Math. J. 13 (2003), no. 4, 61–69.
  • [11] S. S. Dragomir, Some inequalities for the Csiszár '-divergence when ' is an L-Lipschitzian function and applications. Ital. J. Pure Appl. Math. No. 15 (2004), 57–76.
  • [12] S. S. Dragomir, A converse inequality for the Csiszár $\Phi$-divergence. Tamsui Oxf. J. Math. Sci. 20 (2004), no. 1, 35–53.
  • [13] S. S. Dragomir, Some general divergence measures for probability distributions. Acta Math. Hungar. 109 (2005), no. 4, 331–345.
  • [14] S. S. Dragomir, A refinement of Jensen’s inequality with applications for f-divergence measures. Taiwanese J. Math. 14 (2010), no. 1, 153–164.
  • [15] S. S. Dragomir, A generalization of f-divergence measure to convex functions defined on linear spaces. Commun. Math. Anal. 15 (2013), no. 2, 1–14.
  • [16] H. Jeffreys, Theory of Probability, Oxford University Press, 1948, 2nd ed.
  • [17] F. Liese and I. Vajda, Convex Statistical Distances, Teubuer-Texte zur Mathematik, Band 95, Leipzig, 1987.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Silvestru Sever Dragomir

Publication Date September 1, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Dragomir, S. S. (2019). Inequalities for Synchronous Functions and Applications. Constructive Mathematical Analysis, 2(3), 109-123. https://doi.org/10.33205/cma.562166
AMA Dragomir SS. Inequalities for Synchronous Functions and Applications. CMA. September 2019;2(3):109-123. doi:10.33205/cma.562166
Chicago Dragomir, Silvestru Sever. “Inequalities for Synchronous Functions and Applications”. Constructive Mathematical Analysis 2, no. 3 (September 2019): 109-23. https://doi.org/10.33205/cma.562166.
EndNote Dragomir SS (September 1, 2019) Inequalities for Synchronous Functions and Applications. Constructive Mathematical Analysis 2 3 109–123.
IEEE S. S. Dragomir, “Inequalities for Synchronous Functions and Applications”, CMA, vol. 2, no. 3, pp. 109–123, 2019, doi: 10.33205/cma.562166.
ISNAD Dragomir, Silvestru Sever. “Inequalities for Synchronous Functions and Applications”. Constructive Mathematical Analysis 2/3 (September 2019), 109-123. https://doi.org/10.33205/cma.562166.
JAMA Dragomir SS. Inequalities for Synchronous Functions and Applications. CMA. 2019;2:109–123.
MLA Dragomir, Silvestru Sever. “Inequalities for Synchronous Functions and Applications”. Constructive Mathematical Analysis, vol. 2, no. 3, 2019, pp. 109-23, doi:10.33205/cma.562166.
Vancouver Dragomir SS. Inequalities for Synchronous Functions and Applications. CMA. 2019;2(3):109-23.

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