Estimation of f-divergence and Shannon entropy by using Levinson type inequalities for higher order convex functions via Hermite interpolating polynomial

DOI10.1186/s13660-020-02403-yzbMath1503.94015OpenAlexW3032600545MaRDI QIDQ2069442

Muhammad Adeel, Đilda Pečarić, Khuram Ali Khan, Josip E. Pečarić

Publication date: 20 January 2022

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-020-02403-y

zbMATH Keywords

convex functionsinformation theoryLevinson inequality

Mathematics Subject Classification ID

Measures of information, entropy (94A17) Convexity of real functions in one variable, generalizations (26A51) Means (26E60) Information theory (general) (94A15) Inequalities for trigonometric functions and polynomials (26D05)

Related Items (7)

Difference equations related to majorization theorems via Montgomery identity and Green's functions with application to the Shannon entropy ⋮ Estimation of entropies on time scales by Lidstone's interpolation using Csiszár-type functional ⋮ Generalizations of Levinson type inequalities via new Green functions with applications to information theory ⋮ Bounds of some divergence measures using Hermite polynomial via diamond integrals on time scales ⋮ Unnamed Item ⋮ Majorization inequalities via Green functions and Fink's identity with applications to Shannon entropy ⋮ New entropic bounds on time scales via Hermite interpolating polynomial

Cites Work

• Refinement of Jensen's inequality and estimation of \(f\)- and Rényi divergence via Montgomery identity
• Convex functions, partial orderings, and statistical applications
• Theory of statistical inference and information. Transl. from the Slovak by the author
• On Zipf-Mandelbrot entropy
• Common fixed point results in function weighted metric spaces
• Generalization of the Levinson inequality with applications to information theory
• Levinson type inequalities for higher order convex functions via Abel-Gontscharoff interpolation
• Estimation of \(f\)-divergence and Shannon entropy by Levinson-type inequalities via new Green's functions and Lidstone polynomial
• Generalization of an inequality of Ky Fan
• Estimations of \(f\)- and Rényi divergences by using a cyclic refinement of the Jensen's inequality
• On the Green's function of an \(N\)-point boundary value problem
• $f$ -Divergence Inequalities
• Bounds for Shannon and Zipf-Mandelbrot entropies
• Generalized Levinson's inequality and exponential convexity
• Linear operators inequality for $n$-convex functions at a point
• On Choosing and Bounding Probability Metrics
• Generalizations of cyclic refinements of Jensen's inequality by Lidstone's polynomial with applications in information theory
• Bounds for Csiszár divergence and hybrid Zipf‐Mandelbrot entropy
• New bounds for Shannon, relative and Mandelbrot entropies via Abel-Gontscharoff interpolating polynomial
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Estimation of f-divergence and Shannon entropy by using Levinson type inequalities for higher order convex functions via Hermite interpolating polynomial