Generalized Steffensen’s Inequality by Fink’s Identity
Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
RUDN University, Miklukho-Maklaya str. 6, 117198 Moscow, Russia
Author to whom correspondence should be addressed.
Received: 11 February 2019 / Revised: 27 March 2019 / Accepted: 28 March 2019 / Published: 4 April 2019
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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
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
-convex functions at a point. At the end, we present some applications of our study to the theory of exponentially convex functions.
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MDPI and ACS Style
Fahad, A.; Butt, S.I.; Pečarić, J. Generalized Steffensen’s Inequality by Fink’s Identity. Mathematics 2019, 7, 329.
Fahad A, Butt SI, Pečarić J. Generalized Steffensen’s Inequality by Fink’s Identity. Mathematics. 2019; 7(4):329.
Fahad, Asfand; Butt, Saad I.; Pečarić, Josip. 2019. "Generalized Steffensen’s Inequality by Fink’s Identity." Mathematics 7, no. 4: 329.
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