We obtain generalizations of Steffensen’s inequality by using Lidstone’s polynomials. Furthermore, the functionals associated with the obtained generalizations are used to generate n-exponentially and exponentially convex functions, as well as the new Stolarsky-type means.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 11, pp. 1525–1539, November, 2015.
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Pečarić, J., Perušić, A. & Smoljak, K. Generalizations of Steffensen’s Inequality by Lidstone’s Polynomials. Ukr Math J 67, 1721–1738 (2016). https://doi.org/10.1007/s11253-016-1185-6
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DOI: https://doi.org/10.1007/s11253-016-1185-6