A Voronovskaya-type theorem

Authors

  • Mircea Ivan Technical University of Cluj-Napoca, Romania
  • Ioan Raşa Technical University of Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat301-680
Abstract views: 241

Abstract

We give an asymptotic estimation for some sequences of divided differences. We use this estimation to obtain a Voronovskaya-type formula involving linear positive operators.

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References

H. H. Gonska and R. K. Kovacheva, The second order modulus revisited: remarks, applications, problems, Conf. Sem. Mat. Univ. Bari, 257, 1994.

M. Ivan and I. Raşa, A sequence of positive linear operators, Rev. Anal. Numér. Théor. Approx., 24 (1995), 159-164.

E. Neuman, Problem E 2900, Amer. Math. Month., 88 (1981), 538.

E. Neuman and J. Pečarić, Inequalities involving multivariate convex functions, J. Math. Anal. Appl., 137 (1989), 541-549, https://doi.org/10.1016/0022-247x(89)90262-x DOI: https://doi.org/10.1016/0022-247X(89)90262-X

J. Pečarić, An inequality for 3-convex functions, J. Math. Anal. Appl., 90 (1982), 213-218, https://doi.org/10.1016/0022-247x(82)90055-5 DOI: https://doi.org/10.1016/0022-247X(82)90055-5

T. Popoviciu, Introduction à la théorie des différences divisées, Bull. Math. de la Soc. Roumaine des Sci., 42 (1940), 65-78.

T. Popoviciu, Remarques sur le reste de certaines formules d'approximation d'une différence divisée par les dérivées, Buletinul Institutului Politehnic din Iaşi, Serie nouă, 13 (17) (1967), 103-109.

J. Pečarić and I. Raşa, Inequalities for divided differences of n-convex functions, Studia Univ. Babeş-Bolyai, Math., 33 (1990), 7-10.

J. Pečarić and I. Raşa, A linear operator preserving k-convex functions, Bul. Şt. IPCN, 33 (1990), 23-26.

I. Raşa, Korovkin approximation and parabolic functions, Conf. Sem. Mat. Univ. Bari, 236 (1991).

P. C. Sikkema, On some linear positive operators, Indag. Math., 32 (1970), 327-337, https://doi.org/10.1016/s1385-7258(70)80037-3 DOI: https://doi.org/10.1016/S1385-7258(70)80037-3

D. Zwick, A divided difference inequality for n-convex functions, J. Math. Anal. Appl., 104 (1984), 435-436, https://doi.org/10.1016/0022-247x(84)90008-8 DOI: https://doi.org/10.1016/0022-247X(84)90008-8

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Published

2001-02-01

How to Cite

Ivan, M., & Raşa, I. (2001). A Voronovskaya-type theorem. Rev. Anal. Numér. Théor. Approx., 30(1), 47–54. https://doi.org/10.33993/jnaat301-680

Issue

Vol. 30 No. 1 (2001)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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