Generalizations of Steffensen’s Inequality by Lidstone’s Polynomials
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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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- 1.R. P. Agarwal and P. J. Y. Wong, Error Inequalities in Polynomial Interpolation and Their Applications, Kluwer, Dordrecht, etc. (1993).Google Scholar
- 2.K. E. Atkinson, An Introduction to Numerical Analysis, 2nd ed., Wiley, New York, etc. (1989).Google Scholar
- 5.G. J. Lidstone, “Notes on the extension of Aitken’s theorem (for polynomial interpolation) to the Everett types,” Proc. Edinburgh Math. Soc., 2, No. 2, 16–19 (1929).Google Scholar
- 7.J. E. Pečarić, F. Proschan, and Y. L. Tong, “Convex functions, partial orderings, and statistical applications,” Math. Sci. Eng., 187 (1992).Google Scholar
- 10.J. F. Steffensen, “On certain inequalities between mean values and their application to actuarial problems,” Skand. Aktuarietidskr., 82–97 (1918).Google Scholar
- 11.D. V. Widder, The Laplace Transform, Princeton Univ. Press, New Jersey (1941).Google Scholar
- 13.J. M. Whittaker, “On Lidstone series and two-point expansions of analytic functions,” Proc. London Math. Soc., 36, 451–469 (1933-1934).Google Scholar