Levinson type inequalities for higher order convex functions via Abel-Gontscharoff interpolation

DOI10.1186/s13662-019-2360-5zbMath1487.26027OpenAlexW2979338374MaRDI QIDQ2141949

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

Publication date: 25 May 2022

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

Full work available at URL: https://doi.org/10.1186/s13662-019-2360-5

zbMATH Keywords

Green functionsLevinson inequality\(m\)-convex function

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Convexity of real functions in one variable, generalizations (26A51) Means (26E60) Other analytical inequalities (26D20) Inequalities involving other types of functions (26D07)

Related Items (12)

Difference equations related to majorization theorems via Montgomery identity and Green's functions with application to the Shannon entropy ⋮ Estimation of \(f\)-divergence and Shannon entropy by Levinson-type inequalities via new Green's functions and Lidstone polynomial ⋮ A new approach for the derivation of bounds for the Jensen difference ⋮ Some estimations of the Jensen difference and applications ⋮ Generalizations of Levinson type inequalities via new Green functions with applications to information theory ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Levinson-type inequalities via new Green functions and Montgomery identity ⋮ Estimation of f-divergence and Shannon entropy by using Levinson type inequalities for higher order convex functions via Hermite interpolating polynomial ⋮ Majorization inequalities via Green functions and Fink's identity with applications to Shannon entropy ⋮ Some improvements of Jensen's inequality via 4-convexity and applications ⋮ Entropy results for Levinson-type inequalities via Green functions and Hermite interpolating polynomial

Cites Work

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• Linear operators inequality for $n$-convex functions at a point
• Generalization of Jensen's inequality by Lidstone's polynomial and related results
• Some new Ostrowski-type bounds for the Čebyšev functional and applications

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