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 p… Show more
“…In fact, the results presented in [32] provide generalizations of all [10,21,31]. A few other variants of Steffensen's inequality by using interpolating polynomials can be seen in [33][34][35]. Moreover, to elaborate the importance of Hardy-type inequalities in the theory of function spaces, we recommend [36] to the readers.…”
New Steffensen-type inequalities are obtained by combining generalized Taylor expansions, Rabier and Pečarić extensions of Steffensen’s inequality and Faà di Bruno’s formula for higher order derivatives of the composition.
“…In fact, the results presented in [32] provide generalizations of all [10,21,31]. A few other variants of Steffensen's inequality by using interpolating polynomials can be seen in [33][34][35]. Moreover, to elaborate the importance of Hardy-type inequalities in the theory of function spaces, we recommend [36] to the readers.…”
New Steffensen-type inequalities are obtained by combining generalized Taylor expansions, Rabier and Pečarić extensions of Steffensen’s inequality and Faà di Bruno’s formula for higher order derivatives of the composition.
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