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

DOI10.1186/s13660-017-1379-yzbMath1362.26023OpenAlexW2613398519WikidataQ41907930 ScholiaQ41907930MaRDI QIDQ527807

Ravi P. Agarwal, Nasir Mehmood, Saad Ihsan Butt, Josip E. Pečarić

Publication date: 12 May 2017

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

Full work available at URL: https://doi.org/10.1186/s13660-017-1379-y

zbMATH Keywords

Popoviciu inequalityAbel-Gontscharoff interpolating polynomialMontgomery identityGrüss upper boundsnew Green's functionsOstrowski-type bounds

Mathematics Subject Classification ID

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

Related Items (23)

Difference equations related to majorization theorems via Montgomery identity and Green's functions with application to the Shannon entropy ⋮ Hermite-Hadamard type inequalities for fractional integrals via Green's function ⋮ Generalized Steffensen's inequality by Lidstone interpolation and Montogomery's identity ⋮ Generalization of Montgomery identity via Taylor formula on time scales ⋮ New bounds for Shannon, relative and Mandelbrot entropies via Hermite interpolating polynomial ⋮ Generalization of majorization theorem-II ⋮ New converses of Jensen inequality via Green functions with applications ⋮ Extension of Montgomery identity via Taylor polynomial on time scales ⋮ Generalizations of cyclic refinements of Jensen's inequality by Lidstone's polynomial with applications in information theory ⋮ The Popoviciu type inequalities for s-convex functions in the third sense ⋮ New bounds of cyclic Jensen's differences via weighted Hadamard inequalities with applications ⋮ Generalizations of Levinson type inequalities via new Green functions with applications to information theory ⋮ Majorization, ``useful Csiszár divergence and ``useful Zipf-Mandelbrot law ⋮ Unnamed Item ⋮ New bounds for Shannon, relative and Mandelbrot entropies via Abel-Gontscharoff interpolating polynomial ⋮ Generalized Steffensen's inequality by Montgomery identities and Green functions ⋮ Levinson-type inequalities via new Green functions and Montgomery identity ⋮ Quantum Hermite-Hadamard inequality by means of a Green function ⋮ Generalized results of majorization inequality via Lidstone's polynomial and newly Green functions ⋮ Generalized Steffensen's inequality by Montgomery identity ⋮ Several new cyclic Jensen type inequalities and their applications ⋮ Majorization inequalities via Green functions and Fink's identity with applications to Shannon entropy ⋮ 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
• Steffensen inequality, higher order convexity and exponential convexity
• 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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