On generalization of refinement of Jensen's inequality using Fink's identity and Abel-gontscharoff Green function

DOI10.1186/s13660-017-1521-xzbMath1373.26019OpenAlexW2761744257WikidataQ45121155 ScholiaQ45121155MaRDI QIDQ2410510

Tasadduq Niaz, Khuram Ali Khan, Josip E. Pečarić

Publication date: 18 October 2017

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

Full work available at URL: https://doi.org/10.1186/s13660-017-1521-x

zbMATH Keywords

convex functionGreen functionJensen inequalityAbel-Gontscharoff interpolating polynomialFink identitytwo-point right focal problem

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Other analytical inequalities (26D20) Inequalities in real analysis (26D99) Inequalities involving other types of functions (26D07)

Related Items (4)

Levinson type inequalities for higher order convex functions via Abel-Gontscharoff interpolation ⋮ Unnamed Item ⋮ Estimation of different entropies via Hermite interpolating polynomial using Jensen-type functionals ⋮ Estimation of different entropies via Abel–Gontscharoff Green functions and Fink’s identity using Jensen type functionals

Cites Work

• A method to refine the discrete Jensen's inequality for convex and mid-convex functions
• Convex functions, partial orderings, and statistical applications
• A refinement of the discrete Jensen's inequality
• Bounds on the deviation of a function from its averages
• Popoviciu type inequalities via Green function and generalized Montgomery identity
• Some new Ostrowski-type bounds for the Čebyšev functional and applications
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