Several Jensen–Grüss Inequalities with Applications in Information Theory

Several Jensen–Grüss Inequalities with Applications in Information Theory

Several integral Jensen–Grüss inequalities are proved together with their refinements. Some new bounds are obtained for the integral Jensen–Chebyshev inequality. The multidimensional integral versions are also presented. In addition, some integral Jensen–Grüss inequalities for monotone and completel...

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Veröffentlicht in:Ukrainian mathematical journal 2023-05, Vol.74 (12), p.1888-1908
Hauptverfasser: Butt, S. I., Pečarić, Ð., Pečarić, J.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Chebyshev approximation
Entropy (Information theory)
Geometry
Inequalities
Information theory
Mathematics
Mathematics and Statistics
Monotone functions
Statistics
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Zusammenfassung:Several integral Jensen–Grüss inequalities are proved together with their refinements. Some new bounds are obtained for the integral Jensen–Chebyshev inequality. The multidimensional integral versions are also presented. In addition, some integral Jensen–Grüss inequalities for monotone and completely monotone functions are established. Finally, as an application, we present the refinements for Shannon’s entropy.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-023-02176-9