Generalizations of Steffensen’s inequality via two-point Abel-Gontscharoff polynomial

Open access

Abstract

Using two-point Abel-Gontscharoff interpolating polynomial some new generalizations of Steffensen’s inequality for n−convex functions are obtained and some Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using the Čebyšev functional some new bounds for the remainder in obtained generalizations are proven and related Grüss-type inequalities are given.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] R.P. Agarwal P.J.Y. Wong Error Inequalities in Polynomial Interpolation and Their Applications Mathematics and its Applications 262 Kluwer Academic Publishers Dordrecht 1993.

  • [2] P. Cerone S.S. Dragomir Some new bounds for the Čebyšev functional in terms of the first derivative and applications J. Math. Inequal. 8(1) (2014) 159–170.

  • [3] P.J. Davis Interpolation and Approximation Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London 1963.

  • [4] V.L. Gontscharoff Theory of interpolation and approximation of functions Gostekhizdat Moscow 1954.

  • [5] J. Jakšetić J. Pečarić Steffensen’s inequality for positive measures Math. Inequal. Appl. 18(3) (2015) 1159–1170.

  • [6] D.S. Mitrinović The Steffensen inequality Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 247-273 (1969) 1–14.

  • [7] J. Pečarić A. Perušić K. Smoljak Generalizations of Steffensen’s inequality by Abel-Gontscharoff polynomial Khayyam Journal of Mathematics 1(1) (2015) 45–61.

  • [8] J.E. Pečarić F. Proschan Y.L. Tong Convex functions partial orderings and statistical applications Mathematics in science and engineering 187 Academic Press 1992.

  • [9] J. Pečarić K. Smoljak Kalamir S. Varošanec Steffensen’s and related inequalities (A comprehensive survey and recent advances) Monograhps in inequalities 7 Element Zagreb 2014.

  • [10] J.F. Steffensen On certain inequalities between mean values and their application to actuarial problems Skand. Aktuarietids. (1918) 82–97.

  • [11] J.M. Whittaker Interpolatory Function Theory Cambridge University Press London 1935.

Suche
Zeitschrifteninformation
Impact Factor


IMPACT FACTOR 2018: 0.638
5-year IMPACT FACTOR: 0.58

CiteScore 2018: 0.55

SCImago Journal Rank (SJR) 2018: 0.254
Source Normalized Impact per Paper (SNIP) 2018: 0.583

Mathematical Citation Quotient (MCQ) 2018: 0.19

<strong>Zielgruppe:</strong>

researchers in all fields of pure and applied mathematics

Metriken
Gesamte Zeit Letztes Jahr Letzte 30 Tage
Abstract Views 0 0 0
Full Text Views 33 33 5
PDF Downloads 28 28 10