{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T12:05:28Z","timestamp":1762430728436,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2013,4,24]],"date-time":"2013-04-24T00:00:00Z","timestamp":1366761600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Jensen-Shannon, J-divergence and Arithmetic-Geometric mean divergences are three classical divergence measures known in the information theory and statistics literature. These three divergence measures bear interesting inequality among the three non-logarithmic measures known as triangular discrimination, Hellingar\u2019s divergence and symmetric chi-square divergence. However, in 2003, Eve studied seven means from a geometrical point of view, which are Harmonic, Geometric, Arithmetic, Heronian,  Contra-harmonic, Root-mean square and Centroidal. In this paper, we have obtained new inequalities among non-negative differences arising from these seven means. Correlations with generalized triangular discrimination and some new generating measures with their exponential representations are also presented.<\/jats:p>","DOI":"10.3390\/info4020198","type":"journal-article","created":{"date-parts":[[2013,4,24]],"date-time":"2013-04-24T13:19:36Z","timestamp":1366809576000},"page":"198-239","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures"],"prefix":"10.3390","volume":"4","author":[{"given":"Inder","family":"Taneja","sequence":"first","affiliation":[{"name":"Department of Mathematics, Federal University of Santa Catarina, Florian\u00f3polis, SC 88040-900, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2013,4,24]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Refinement inequalities among symmetric divergence measures","volume":"2","author":"Taneja","year":"2005","journal-title":"Austr. 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Asymptotic Methods in Statistical Decision Theory, Springer.","DOI":"10.1007\/978-1-4612-4946-7"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1515\/crll.1909.136.210","article-title":"Neue Begr\u00fcndung der Theorie der quadratischen Formen von unendlichen vielen Ver\u00e4nderlichen","volume":"136","author":"Hellinger","year":"1909","journal-title":"J. Reine Aug. Math."},{"key":"ref_7","unstructured":"Taneja, I.J. Inequalities having seven means and proportionality relations. Available online:http:\/\/arxiv.org\/abs\/1203.2288\/."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.ins.2003.11.002","article-title":"Relative information of type s, Csiszar\u2019s f-divergence, and information inequalities","volume":"166","author":"Taneja","year":"2004","journal-title":"Inf. Sci."},{"key":"ref_9","first-page":"357","article-title":"Refinement of inequalities among means","volume":"31","author":"Taneja","year":"2006","journal-title":"J. Combin. Inf. Syst. Sci."},{"key":"ref_10","first-page":"85","article-title":"On symmetric information divergence measures of Csiszar\u2019s f-divergence class","volume":"3","author":"Jain","year":"2007","journal-title":"J. Appl. Math. Stat. Inf."},{"key":"ref_11","first-page":"1","article-title":"On a symmetric divergence measure and information inequalities","volume":"6","author":"Kumar","year":"2005","journal-title":"J. Inequal. Pure Appl. Math."},{"key":"ref_12","first-page":"91","article-title":"Bounds on triangular discrimination, harmonic mean and symmetric chi-square divergences","volume":"4","author":"Taneja","year":"2006","journal-title":"J. Concr. Appl. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1602","DOI":"10.1109\/18.850703","article-title":"Some inequalities for information divergence and related measures of discrimination","volume":"46","author":"Topsoe","year":"2000","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","first-page":"295","article-title":"New inequalities for jefferys divergence measure","volume":"16","author":"Dragomir","year":"2000","journal-title":"Tamsui Oxf. J. Math. Sci."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/4\/2\/198\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:46:21Z","timestamp":1760219181000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/4\/2\/198"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,24]]},"references-count":14,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,6]]}},"alternative-id":["info4020198"],"URL":"https:\/\/doi.org\/10.3390\/info4020198","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2013,4,24]]}}}