Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, , 140 - 154, 18.12.2023
https://doi.org/10.32323/ujma.1362709

Öz

Kaynakça

  • [1] I. Csiszar, Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizitat von Markoffschen Ketten, (German), Magyar Tud. Akad. Mat. Kutato Int. Kozl., 8 (1963), 85–108.
  • [2] P. Cerone, S. S. Dragomir, F. Osterreicher, Bounds on extended f -divergences for a variety of classes, Kybernetika (Prague), 40(6) (2004), 745–756.
  • [3] P. Kafka, F. Osterreicher, I. Vincze, On powers of f -divergence defining a distance, Studia Sci. Math. Hungar., 26 (1991), 415–422.
  • [4] F. Osterreicher, I. Vajda, A new class of metric divergences on probability spaces and its applicability in statistics, Ann. Inst. Statist. Math., 55(3) (2003), 639–653.
  • [5] F. Liese, I. Vajda, Convex Statistical Distances, Teubuer–Texte zur Mathematik, Band, 95, Leipzig, (1987).
  • [6] P. Cerone, S. S. Dragomir, Approximation of the integral mean divergence and f -divergence via mean results, Math. Comput. Modelling, 42(1-2) (2005), 207–219.
  • [7] S. S. Dragomir, Some inequalities for (m;M)-convex mappings and applications for the Csisz´ar F-divergence in information theory, Math. J. Ibaraki Univ., 33 (2001), 35–50.
  • [8] S. S. Dragomir, Some inequalities for two Csisz´ar divergences and applications, Mat. Bilten, 25 (2001), 73–90.
  • [9] S. S. Dragomir, An upper bound for the Csiszar f-divergence in terms of the variational distance and applications, Panamer. Math. J. 12 (2002), no. 4, 43–54.
  • [10] S. S. Dragomir, An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Inequal. Pure and Appl. Math., 3(2) (2002), Art. 31.
  • [11] S. S. Dragomir, An inequality improving the second Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Inequal. Pure and Appl. Math., 3(3) (2002), Art. 35.
  • [12] S. S. Dragomir, Upper and lower bounds for Csiszar f -divergence in terms of Hellinger discrimination and applications, Nonlinear Anal. Forum, 7(1) (2002), 1–13.
  • [13] S. S. Dragomir, Bounds for f -divergences under likelihood ratio constraints, Appl. Math., 48(3) (2003), 205–223.
  • [14] S. S. Dragomir, New inequalities for Csiszar divergence and applications, Acta Math. Vietnam., 28(2) (2003), 123–134.
  • [15] S. S. Dragomir, A generalized f -divergence for probability vectors and applications, Panamer. Math. J., 13(4) (2003), 61–69.
  • [16] S. S. Dragomir, Some inequalities for the Csiszar j-divergence when j is an L-Lipschitzian function and applications, Ital. J. Pure Appl. Math., 15 (2004), 57–76.
  • [17] S. S. Dragomir, A converse inequality for the Csiszar F-divergence, Tamsui Oxf. J. Math. Sci., 20(1) (2004), 35–53.
  • [18] S. S. Dragomir, Some general divergence measures for probability distributions, Acta Math. Hungar., 109(4) (2005), 331–345.
  • [19] S. S. Dragomir, Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc., 74(3)(2006), 471–476.
  • [20] S. S. Dragomir, A refinement of Jensen’s inequality with applications for f -divergence measures, Taiwanese J. Math., 14(1) (2010), 153–164.
  • [21] J. Burbea, C. R. Rao, On the convexity of some divergence measures based on entropy functions, IEEE Tran. Inf. Theor., Vol. IT-28(3) (1982), 489–495.
  • [22] S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, (2000), https://rgmia.org/papers/monographs/Master.pdf.

Some $f$-Divergence Measures Related to Jensen's One

Yıl 2023, , 140 - 154, 18.12.2023
https://doi.org/10.32323/ujma.1362709

Öz

In this paper, we introduce some $f$-divergence measures that are related to the Jensen's divergence introduced by Burbea and Rao in 1982. We establish their joint convexity and provide some inequalities between these measures and a combination of Csisz\'{a}r's $f$-divergence, $f$-midpoint divergence and $f$-integral divergence measures.

Kaynakça

  • [1] I. Csiszar, Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizitat von Markoffschen Ketten, (German), Magyar Tud. Akad. Mat. Kutato Int. Kozl., 8 (1963), 85–108.
  • [2] P. Cerone, S. S. Dragomir, F. Osterreicher, Bounds on extended f -divergences for a variety of classes, Kybernetika (Prague), 40(6) (2004), 745–756.
  • [3] P. Kafka, F. Osterreicher, I. Vincze, On powers of f -divergence defining a distance, Studia Sci. Math. Hungar., 26 (1991), 415–422.
  • [4] F. Osterreicher, I. Vajda, A new class of metric divergences on probability spaces and its applicability in statistics, Ann. Inst. Statist. Math., 55(3) (2003), 639–653.
  • [5] F. Liese, I. Vajda, Convex Statistical Distances, Teubuer–Texte zur Mathematik, Band, 95, Leipzig, (1987).
  • [6] P. Cerone, S. S. Dragomir, Approximation of the integral mean divergence and f -divergence via mean results, Math. Comput. Modelling, 42(1-2) (2005), 207–219.
  • [7] S. S. Dragomir, Some inequalities for (m;M)-convex mappings and applications for the Csisz´ar F-divergence in information theory, Math. J. Ibaraki Univ., 33 (2001), 35–50.
  • [8] S. S. Dragomir, Some inequalities for two Csisz´ar divergences and applications, Mat. Bilten, 25 (2001), 73–90.
  • [9] S. S. Dragomir, An upper bound for the Csiszar f-divergence in terms of the variational distance and applications, Panamer. Math. J. 12 (2002), no. 4, 43–54.
  • [10] S. S. Dragomir, An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Inequal. Pure and Appl. Math., 3(2) (2002), Art. 31.
  • [11] S. S. Dragomir, An inequality improving the second Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Inequal. Pure and Appl. Math., 3(3) (2002), Art. 35.
  • [12] S. S. Dragomir, Upper and lower bounds for Csiszar f -divergence in terms of Hellinger discrimination and applications, Nonlinear Anal. Forum, 7(1) (2002), 1–13.
  • [13] S. S. Dragomir, Bounds for f -divergences under likelihood ratio constraints, Appl. Math., 48(3) (2003), 205–223.
  • [14] S. S. Dragomir, New inequalities for Csiszar divergence and applications, Acta Math. Vietnam., 28(2) (2003), 123–134.
  • [15] S. S. Dragomir, A generalized f -divergence for probability vectors and applications, Panamer. Math. J., 13(4) (2003), 61–69.
  • [16] S. S. Dragomir, Some inequalities for the Csiszar j-divergence when j is an L-Lipschitzian function and applications, Ital. J. Pure Appl. Math., 15 (2004), 57–76.
  • [17] S. S. Dragomir, A converse inequality for the Csiszar F-divergence, Tamsui Oxf. J. Math. Sci., 20(1) (2004), 35–53.
  • [18] S. S. Dragomir, Some general divergence measures for probability distributions, Acta Math. Hungar., 109(4) (2005), 331–345.
  • [19] S. S. Dragomir, Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc., 74(3)(2006), 471–476.
  • [20] S. S. Dragomir, A refinement of Jensen’s inequality with applications for f -divergence measures, Taiwanese J. Math., 14(1) (2010), 153–164.
  • [21] J. Burbea, C. R. Rao, On the convexity of some divergence measures based on entropy functions, IEEE Tran. Inf. Theor., Vol. IT-28(3) (1982), 489–495.
  • [22] S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, (2000), https://rgmia.org/papers/monographs/Master.pdf.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematikte Optimizasyon, Sayısal ve Hesaplamalı Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Sever Dragomır 0000-0003-2902-6805

Erken Görünüm Tarihi 22 Kasım 2023
Yayımlanma Tarihi 18 Aralık 2023
Gönderilme Tarihi 19 Eylül 2023
Kabul Tarihi 19 Kasım 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Dragomır, S. (2023). Some $f$-Divergence Measures Related to Jensen’s One. Universal Journal of Mathematics and Applications, 6(4), 140-154. https://doi.org/10.32323/ujma.1362709
AMA Dragomır S. Some $f$-Divergence Measures Related to Jensen’s One. Univ. J. Math. Appl. Aralık 2023;6(4):140-154. doi:10.32323/ujma.1362709
Chicago Dragomır, Sever. “Some $f$-Divergence Measures Related to Jensen’s One”. Universal Journal of Mathematics and Applications 6, sy. 4 (Aralık 2023): 140-54. https://doi.org/10.32323/ujma.1362709.
EndNote Dragomır S (01 Aralık 2023) Some $f$-Divergence Measures Related to Jensen’s One. Universal Journal of Mathematics and Applications 6 4 140–154.
IEEE S. Dragomır, “Some $f$-Divergence Measures Related to Jensen’s One”, Univ. J. Math. Appl., c. 6, sy. 4, ss. 140–154, 2023, doi: 10.32323/ujma.1362709.
ISNAD Dragomır, Sever. “Some $f$-Divergence Measures Related to Jensen’s One”. Universal Journal of Mathematics and Applications 6/4 (Aralık 2023), 140-154. https://doi.org/10.32323/ujma.1362709.
JAMA Dragomır S. Some $f$-Divergence Measures Related to Jensen’s One. Univ. J. Math. Appl. 2023;6:140–154.
MLA Dragomır, Sever. “Some $f$-Divergence Measures Related to Jensen’s One”. Universal Journal of Mathematics and Applications, c. 6, sy. 4, 2023, ss. 140-54, doi:10.32323/ujma.1362709.
Vancouver Dragomır S. Some $f$-Divergence Measures Related to Jensen’s One. Univ. J. Math. Appl. 2023;6(4):140-54.

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