Naslov
On Generalization of Refinement of Jensen's Inequality Using Fink's Identity and Abel- Gontscharoff Green function

Autori
Niaz, Tasadduq ; Khan, Khuram Ali ; Pečarić, Josip

Izvornik
Journal of inequalities and applications (1029-242X) 2017 (2017), 254; 1-12

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
convex function ; Jensen’s inequality ; Fink’s identity ; Abel-Gontscharoff interpolating polynomial ; Green function for ‘two-point right focal’ problem

Sažetak
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 Pecari ˇ c 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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