Generalized Steffensen’s Inequality by Fink’s Identity

Asfand Fahad, Saad Ihsan Butt and Josip Pečarić
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Asfand Fahad: Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan
Saad Ihsan Butt: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
Josip Pečarić: RUDN University, Miklukho-Maklaya str. 6, 117198 Moscow, Russia

Mathematics, 2019, vol. 7, issue 4, 1-18

Abstract: 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.

Keywords: Steffensen’s inequality; higher order convexity; Green functions; Montgomery identity; Fink’s identity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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