Research Article
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Year 2019, Volume 2, Issue 3, 109 - 123, 01.09.2019
https://doi.org/10.33205/cma.562166

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
https://doi.org/10.33205/cma.562166

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.

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.

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

Silvestru Sever DRAGOMİR>
Victoria University
Australia

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

Cite

Bibtex @research article { cma562166, journal = {Constructive Mathematical Analysis}, issn = {2651-2939}, address = {}, publisher = {Tuncer ACAR}, year = {2019}, volume = {2}, number = {3}, pages = {109 - 123}, doi = {10.33205/cma.562166}, title = {Inequalities for Synchronous Functions and Applications}, key = {cite}, author = {Dragomir, Silvestru Sever} }
APA Dragomir, S. S. (2019). Inequalities for Synchronous Functions and Applications . Constructive Mathematical Analysis , 2 (3) , 109-123 . DOI: 10.33205/cma.562166
MLA Dragomir, S. S. "Inequalities for Synchronous Functions and Applications" . Constructive Mathematical Analysis 2 (2019 ): 109-123 <https://dergipark.org.tr/en/pub/cma/issue/45605/562166>
Chicago Dragomir, S. S. "Inequalities for Synchronous Functions and Applications". Constructive Mathematical Analysis 2 (2019 ): 109-123
RIS TY - JOUR T1 - Inequalities for Synchronous Functions and Applications AU - Silvestru SeverDragomir Y1 - 2019 PY - 2019 N1 - doi: 10.33205/cma.562166 DO - 10.33205/cma.562166 T2 - Constructive Mathematical Analysis JF - Journal JO - JOR SP - 109 EP - 123 VL - 2 IS - 3 SN - 2651-2939- M3 - doi: 10.33205/cma.562166 UR - https://doi.org/10.33205/cma.562166 Y2 - 2019 ER -
EndNote %0 Constructive Mathematical Analysis Inequalities for Synchronous Functions and Applications %A Silvestru Sever Dragomir %T Inequalities for Synchronous Functions and Applications %D 2019 %J Constructive Mathematical Analysis %P 2651-2939- %V 2 %N 3 %R doi: 10.33205/cma.562166 %U 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
AMA Dragomir S. S. Inequalities for Synchronous Functions and Applications. CMA. 2019; 2(3): 109-123.
Vancouver Dragomir S. S. Inequalities for Synchronous Functions and Applications. Constructive Mathematical Analysis. 2019; 2(3): 109-123.
IEEE S. S. Dragomir , "Inequalities for Synchronous Functions and Applications", Constructive Mathematical Analysis, vol. 2, no. 3, pp. 109-123, Sep. 2019, doi:10.33205/cma.562166

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