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

The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green’s functions. New generalizations of an improved Popoviciu inequality are obtained by using generalized Montgomery identity along with new G...

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Detalles Bibliográficos
Autores principales: Mehmood, Nasir, Agarwal, Ravi P, Butt, Saad Ihsan, Pečarić, Josip
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5423991/
https://www.ncbi.nlm.nih.gov/pubmed/28553058
http://dx.doi.org/10.1186/s13660-017-1379-y
Descripción
Sumario:The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green’s functions. New generalizations of an improved Popoviciu inequality are obtained by using generalized Montgomery identity along with new Green’s functions. As an application, we formulate the monotonicity of linear functionals constructed from the generalized identities, utilizing the recent theory of inequalities for n-convex functions at a point. New upper bounds of Grüss and Ostrowski type are also computed.

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