Some inequalities for Csiszár divergence via theory of time scales

DOI10.1186/s13662-020-03159-xzbMath1485.26021OpenAlexW3112120235MaRDI QIDQ2668826

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

Publication date: 7 March 2022

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

Full work available at URL: https://doi.org/10.1186/s13662-020-03159-x

zbMATH Keywords

convex functionquantum calculusCsiszár divergencetime scales calculus

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Inequalities for sums, series and integrals (26D15) Difference equations, scaling ((q)-differences) (39A13) Inequalities involving derivatives and differential and integral operators (26D10) Real analysis on time scales or measure chains (26E70)

Related Items (7)

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 related to Csiszár divergence via diamond integral 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

• Integral inequalities on time scales via the theory of isotonic linear functionals
• Some nonlinear dynamic integral inequalities on time scales
• Theory of statistical inference and information. Transl. from the Slovak by the author
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• On Zipf-Mandelbrot entropy
• Shannon type inequalities via time scales theory
• On the boundedness of a class of nonlinear dynamic equations of second order
• Estimations of \(f\)- and Rényi divergences by using a cyclic refinement of the Jensen's inequality
• Inequalities on Time Scales: A Survey
• $f$ -Divergence Inequalities
• Nonlinear retarded integral inequalities on time scales and their applications
• On Choosing and Bounding Probability Metrics
• Some nonlinear dynamic inequalities on time scales
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