2011/04/30 by Shigeru Furuichi, S. Furuichi, Flavia‐Corina Mitroi‐Symeonidis +2 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Mathematical Inequalities and Applications #Statistical Mechanics and Entropy #cond-mat.stat-mech #cs.IT #math.CA #math.IT #msc:26D15 #msc:94A17
paper · pdf · doi:10.1016/j.physa.2011.07.052
published as Physica A 391 (2012) 388--400 · 18 pages
openalex publication_date 2011/08/22 · crossref created 2011/08/22 · arxiv created 2011/10/18 · arxiv updated 2011/10/19 · crossref issued 2012/01/01 · crossref published 2012/01/01 · crossref published-print 2012/01/01 · crossref deposited 2025/10/08 · openalex created_date 2025/10/10 · crossref indexed 2026/01/03 · openalex updated_date 2026/07/28
Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some parametric extended divergences combining Jeffreys divergence and Tsallis entropy defined by generalized logarithmic functions, which lead to new inequalities. In addition, we give lower bounds for one-parameter extended Fermi-Dirac and Bose-Einstein divergences. Finally, we establish some inequalities for the Tsallis entropy, the Tsallis relative entropy and some divergences by the use of the Young's inequality.