On generalization of refinement of Jensen’s inequality using Fink’s identity and Abel-Gontscharoff Green function View Full Text


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Article Info

DATE

2017-10-10

AUTHORS

Tasadduq Niaz, Khuram Ali Khan, Josip Pečarić

ABSTRACT

In this paper, we formulate new Abel-Gontscharoff type identities involving new Green functions for the 'two-point right focal' problem. We use Fink's identity and a new Abel-Gontscharoff-type Green's function for a 'two-point right focal' to generalize the refinement of Jensen's inequality given in (Horváth and Pečarić in Math. Inequal. Appl. 14: 777-791, 2011) from convex function to higher order convex function. Also we formulate the monotonicity of the linear functional obtained from these identities using the recent theory of inequalities for n-convex function at a point. Further we give the bounds for the identities related to the generalization of the refinement of Jensen's inequality using inequalities for the Cebyšev functional. Some results relating to the Grüss and Ostrowski-type inequalities are constructed. More... »

PAGES

254

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s13660-017-1521-x

DOI

http://dx.doi.org/10.1186/s13660-017-1521-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1092156257

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/29070937


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