Improvements of Jensen's inequality and its converse for strongly convex functions with applications to strongly f-divergences
In this paper, using the class of strongly convex functions, which is subclass of convex functions with stronger versions of analogous properties, we get improvements of Jessen's and Jensen's inequalities, their converses as well as related Jensen-type interpolating inequalities which pres...
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| Vydané v: | Journal of mathematical analysis and applications Ročník 531; číslo 2; s. 127866 |
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| Jazyk: | English |
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15.03.2024
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| ISSN: | 0022-247X, 1096-0813 |
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| Abstract | In this paper, using the class of strongly convex functions, which is subclass of convex functions with stronger versions of analogous properties, we get improvements of Jessen's and Jensen's inequalities, their converses as well as related Jensen-type interpolating inequalities which present a starting point in many significant results in recent investigations. Obtained improvements we apply to so called strongly f-divergences, a concept of f-divergences for strongly convex functions. As outcome we derive stronger estimates for some well known divergences as the Kullback-Leibler divergence, χ2-divergence, Hellinger divergence, Bhattacharya distance and Jeffreys distance. |
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| AbstractList | In this paper, using the class of strongly convex functions, which is subclass of convex functions with stronger versions of analogous properties, we get improvements of Jessen's and Jensen's inequalities, their converses as well as related Jensen-type interpolating inequalities which present a starting point in many significant results in recent investigations. Obtained improvements we apply to so called strongly f-divergences, a concept of f-divergences for strongly convex functions. As outcome we derive stronger estimates for some well known divergences as the Kullback-Leibler divergence, χ2-divergence, Hellinger divergence, Bhattacharya distance and Jeffreys distance. |
| ArticleNumber | 127866 |
| Author | Ivelić Bradanović, Slavica |
| Author_xml | – sequence: 1 givenname: Slavica surname: Ivelić Bradanović fullname: Ivelić Bradanović, Slavica email: sivelic@gradst.hr organization: Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Matice Hrvatske 15, 21000 Split, Croatia |
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| Keywords | Csiszár f-divergence Jensen's inequality Strongly convex functions Strongly f-divergences Kullback-Leibler divergence Jessen's inequality |
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| References | Klaričić Bakula, Nikodem (br0140) 2016; 434 Jessen (br0190) 1931 Polyak (br0290) 1966; 7 Klaričić Bakula, Pečarić, Perić (br0150) 2012; 218 Nikodem (br0270) 2014 Lovričević, Pečarić, Pečarić (br0210) 2018; 36 Beesack, Pečarić (br0010) 1985; 110 Lugosi, Neu (br0220) 2022; 178 Dragomir (br0070) 2014; 16 Pečarić, Proschan, Tong (br0280) 1992 Ivelić, Pečarić (br0180) 2011; 5 Csiszár, Körner (br0040) 1981 Polyanskiy, Wu (br0300) 2022 Merentes, Nikodem (br0240) 2010; 80 Čuljak, Ivanković, Pečarić (br0050) 2009; 58 Ivelić Bradanović (br0170) 2019; 43 Melbourne (br0230) 2020; 11 Gavrea, Jakšetić, Pečarić (br0120) 2009; 50 Lah, Ribarič (br0200) 1973; 453 Roberts, Varberg (br0310) 1973 Sason (br0320) 2022; 5 Sason, Verdu (br0330) 2016; 11 Hiriart-Urruty, Lemaréchal (br0130) 1993 Crooks (br0020) 2017 Dragomir (br0100) 2000 Mitrinović, Pečarić, Fink (br0260) 1993 Dragomir (br0080) 2006; 74 Krnić, Lovričević, Pečarić, Perić (br0160) 2015 Mitroi-Symeonidis, Minculete (br0250) 2018; 41 Daniels, Maunu, Hand (br0060) 2021; 34 Dragomir (br0090) 2000 Csiszár (br0030) 1967; 2 Dragomir (br0110) 2001; 33 Klaričić Bakula (10.1016/j.jmaa.2023.127866_br0140) 2016; 434 Polyanskiy (10.1016/j.jmaa.2023.127866_br0300) 2022 Lah (10.1016/j.jmaa.2023.127866_br0200) 1973; 453 Merentes (10.1016/j.jmaa.2023.127866_br0240) 2010; 80 Čuljak (10.1016/j.jmaa.2023.127866_br0050) 2009; 58 Hiriart-Urruty (10.1016/j.jmaa.2023.127866_br0130) 1993 Mitroi-Symeonidis (10.1016/j.jmaa.2023.127866_br0250) 2018; 41 Csiszár (10.1016/j.jmaa.2023.127866_br0030) 1967; 2 Dragomir (10.1016/j.jmaa.2023.127866_br0110) 2001; 33 Nikodem (10.1016/j.jmaa.2023.127866_br0270) 2014 Mitrinović (10.1016/j.jmaa.2023.127866_br0260) 1993 Crooks (10.1016/j.jmaa.2023.127866_br0020) 2017 Dragomir (10.1016/j.jmaa.2023.127866_br0100) 2000 Lovričević (10.1016/j.jmaa.2023.127866_br0210) 2018; 36 Sason (10.1016/j.jmaa.2023.127866_br0320) 2022; 5 Csiszár (10.1016/j.jmaa.2023.127866_br0040) 1981 Sason (10.1016/j.jmaa.2023.127866_br0330) 2016; 11 Dragomir (10.1016/j.jmaa.2023.127866_br0090) 2000 Ivelić Bradanović (10.1016/j.jmaa.2023.127866_br0170) 2019; 43 Daniels (10.1016/j.jmaa.2023.127866_br0060) 2021; 34 Lugosi (10.1016/j.jmaa.2023.127866_br0220) 2022; 178 Jessen (10.1016/j.jmaa.2023.127866_br0190) 1931 Pečarić (10.1016/j.jmaa.2023.127866_br0280) 1992 Ivelić (10.1016/j.jmaa.2023.127866_br0180) 2011; 5 Gavrea (10.1016/j.jmaa.2023.127866_br0120) 2009; 50 Melbourne (10.1016/j.jmaa.2023.127866_br0230) 2020; 11 Dragomir (10.1016/j.jmaa.2023.127866_br0080) 2006; 74 Beesack (10.1016/j.jmaa.2023.127866_br0010) 1985; 110 Krnić (10.1016/j.jmaa.2023.127866_br0160) 2015 Dragomir (10.1016/j.jmaa.2023.127866_br0070) 2014; 16 Polyak (10.1016/j.jmaa.2023.127866_br0290) 1966; 7 Roberts (10.1016/j.jmaa.2023.127866_br0310) 1973 Klaričić Bakula (10.1016/j.jmaa.2023.127866_br0150) 2012; 218 |
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| SubjectTerms | Csiszár f-divergence Jensen's inequality Jessen's inequality Kullback-Leibler divergence Strongly convex functions Strongly f-divergences |
| Title | Improvements of Jensen's inequality and its converse for strongly convex functions with applications to strongly f-divergences |
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