Article

Generalizations of Steffensen’s inequality by Lidstone’s polynomial and related results

Published in: Quaestiones Mathematicae
Volume 43 , issue 3 , 2020 , pages: 293–307

DOI: 10.2989/16073606.2018.1539048

Author(s): Josip Pečarić Faculty of Textile Technology, Croatia , Anamarija Perušić Pribanić Faculty of Civil Engineering, Croatia , Ana Vukelić Faculty of Food Technology and Biotechnology, Croatia

Keywords: Primary 26D15 , Secondary 26A51 , Primary 26D15 , Secondary 26A51

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Abstract

In this paper we obtain few valuable identities by using Lidstone’s polynomial. Further, the identities were applied for constructing new generalizations of Steﬀensen’s inequality, namely for (2n)−convex and (2n + 1)−convex functions. In addition, using Čebyšev and Grüss type inequalities we consider the bounds for the integrals in the perturben versions of the previously described identities. Moreover, related Ostrowski type inequalities are given.

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