New generalizations of Popoviciu type inequalities via new Green functions and Fink's identity

DOI10.1016/j.trmi.2017.04.003zbMath1373.26024OpenAlexW2614474551MaRDI QIDQ2409659

Saad Ihsan Butt, Nasir Mehmood, Josip E. Pečarić

Publication date: 13 October 2017

Published in: Transactions of A. Razmadze Mathematical Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.trmi.2017.04.003

zbMATH Keywords

Popoviciu inequalityAbel-Gontscharoff interpolating polynomialGrüss upper boundsOstrowski-type boundsnew Green functionsFink identity

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15)

Related Items (8)

Refinement of Jensen's inequality and estimation of \(f\)- and Rényi divergence via Montgomery identity ⋮ 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 ⋮ Unnamed Item ⋮ Estimation of different entropies via Lidstone polynomial using Jensen-type functionals ⋮ Estimation of different entropies via Hermite interpolating polynomial using Jensen-type functionals ⋮ New entropic bounds on time scales via Hermite interpolating polynomial ⋮ Estimation of different entropies via Abel–Gontscharoff Green functions and Fink’s identity using Jensen type functionals

Cites Work

• Generalization of Popoviciu-type inequalities via Fink identity
• New extensions of Popoviciu's inequality
• Popoviciu's inequality for functions of several variables
• Convex functions, partial orderings, and statistical applications
• Explicit error estimates for quintic and biquintic spline interpolation. II
• Steffensen inequality, higher order convexity and exponential convexity
• Bounds on the deviation of a function from its averages
• The integral version of Popoviciu's inequality
• Linear operators inequality for $n$-convex functions at a point
• Popoviciu type inequalities via Green function and generalized Montgomery identity
• Popoviciu type inequalities via Green function and Taylor polynomial
• Some new Ostrowski-type bounds for the Čebyšev functional and applications
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