Shannon type inequalities via time scales theory

DOI10.1186/s13662-020-02587-zzbMath1482.39037OpenAlexW3031557181MaRDI QIDQ2058189

Đilda Pečarić, Iqrar Ansari, Ammara Nosheen, Khuram Ali Khan, Josip E. Pečarić

Publication date: 7 December 2021

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-020-02587-z

zbMATH Keywords

convex functionShannon entropytime scale calculus

Mathematics Subject Classification ID

Time-scale analysis and singular perturbations in control/observation systems (93C70) Functional inequalities, including subadditivity, convexity, etc. (39B62) Measures of information, entropy (94A17) Real analysis on time scales or measure chains (26E70)

Related Items (8)

Estimation of entropies on time scales by Lidstone's interpolation using Csiszár-type functional ⋮ Estimation of divergence measures on time scales via Taylor's polynomial and Green's function with applications in \(q\)-calculus ⋮ Estimation of divergences on time scales via the Green function and Fink's identity ⋮ Some inequalities for Csiszár divergence via theory of time scales ⋮ Generalizations of Shannon type inequalities via diamond integrals on time scales ⋮ Generalization of some bounds containing entropies on time scales ⋮ Estimation of divergence measures via Weighted Jensen inequality on time scales ⋮ New entropic bounds on time scales via Hermite interpolating polynomial

Cites Work

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• Majorization, Csiszár divergence and Zipf-Mandelbrot law
• Estimations of \(f\)- and Rényi divergences by using a cyclic refinement of the Jensen's inequality
• Multiple Lebesgue integration on time scales
• Inequalities on Time Scales: A Survey
• Bounds for Shannon and Zipf-Mandelbrot entropies
• Some properties of Zipf-Mandelbrot law and Hurwitz ζ-function

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