Generalized Steffensen’s Inequality by Fink’s Identity

By using Fink’s Identity, Green functions, and Montgomery identities we prove some identities related to Steffensen’s inequality. Under the assumptions of n-convexity and n-concavity, we give new generalizations of Steffensen’s inequality and its reverse. Generalizations of some inequalities (and th...

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Bibliographic Details
Published in:Mathematics (Basel) 2019-04, Vol.7 (4), p.329
Main Authors: Fahad, Asfand, Butt, Saad Ihsan, Pečarić, Josip
Format: Article
Language:English
Subjects:
Concavity
Convex analysis
Convexity
Fink’s identity
Food science
Green functions
Green's functions
higher order convexity
Identities
Inequalities
Inequality
Montgomery identity
Steffensen’s inequality
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Summary:By using Fink’s Identity, Green functions, and Montgomery identities we prove some identities related to Steffensen’s inequality. Under the assumptions of n-convexity and n-concavity, we give new generalizations of Steffensen’s inequality and its reverse. Generalizations of some inequalities (and their reverse), which are related to Hardy-type inequality. New bounds of Gr u ¨ ss and Ostrowski-type inequalities have been proved. Moreover, we formulate generalized Steffensen’s-type linear functionals and prove their monotonicity for the generalized class of ( n + 1 ) -convex functions at a point. At the end, we present some applications of our study to the theory of exponentially convex functions.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7040329