Estimation of divergence measures via weighted Jensen inequality on time scales

The main purpose of the presented paper is to obtain some time scale inequalities for different divergences and distances by using weighted time scales Jensen’s inequality. These results offer new inequalities in h -discrete calculus and quantum calculus and extend some known results in the literatu...

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Bibliographic Details
Published in:Journal of inequalities and applications 2021-05, Vol.2021 (1), p.1-21, Article 93
Main Authors: Ansari, Iqrar, Khan, Khuram Ali, Nosheen, Ammara, Pečarić, Ðilda, Pečarić, Josip
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Balances (scales)
Csiszár divergence
Inequalities
Jensen’s inequality
Lower bounds
Mathematics
Mathematics and Statistics
Time
Time scales
Zipf and Zipf–Mandelbrot law
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Summary:The main purpose of the presented paper is to obtain some time scale inequalities for different divergences and distances by using weighted time scales Jensen’s inequality. These results offer new inequalities in h -discrete calculus and quantum calculus and extend some known results in the literature. The lower bounds of some divergence measures are also presented. Moreover, the obtained discrete results are given in the light of the Zipf–Mandelbrot law and the Zipf law.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-021-02630-x