Some general Kantorovich type operators

Authors

  • Petru I. Braica Secondary School Grigore Moisil, Satu Mare, Romania
  • Ovidiu T. Pop National College "Mihai Eminescu", Satu Mare, Romania

DOI:

https://doi.org/10.33993/jnaat412-973

Keywords:

Kantorovich operators, approximation and convergence theorem, Voronovskaja-type theorem
Abstract views: 242

Abstract

A general class of linear and positive operators of Kantorovich-type is constructed. The operators of this type which preserve exactly two test functions from the set \(\{e_0, e_1, e_2\}\) are determined and their approximation properties and convergence theorems are studied.

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References

O. Agratini, An asymptotic formula for a class of approximation processes of King's type, Studia Sci. Math. Hungar, 47 (2010) No. 4, pp. 435-444, https://doi.org/10.1556/sscmath.2009.1142 DOI: https://doi.org/10.1556/sscmath.2009.1142

P.I. Braica, O. T.Pop and A. D. Indrea, About a King-type operator, Appl. Math. Inf. Sci., 6 (2012) No. 1, pp. 145-148.

L.V. Kantorovich, Sur certain développements suivant les polinômes de la forme de S. Bernstein, C. R. Acad. URSS, I, II (1930), pp. 563-568, pp. 595-600.

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O.T. Pop, About some linear and positive operators defined by infinite sum, Dem. Math., XXXIX (2006) No. 2, pp. 377-388, https://doi.org/10.1515/dema-2006-0216 DOI: https://doi.org/10.1515/dema-2006-0216

O.T. Pop, D. Bărbosu and P.I. Braica, Some general linears and positive operators (to appear)

O.T. Pop, The generalization of Voronovskaja's theorem for a class of linear and positive operators, Rev. Anal. Numér. Théor. Approx., 34 (2005), pp. 79-91, http://ictp.acad.ro/jnaat/journal/article/view/2005-vol34-no1-art9

E. Voronovskaja, Détermination de la forme asymptotique d'approximation des fonctions par les polynômes de S. N. Bernstein, C. R. Acad. Sci. URSS, 1932, pp. 79-85.

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Published

2012-08-01

How to Cite

Braica, P. I., & Pop, O. T. (2012). Some general Kantorovich type operators. Rev. Anal. Numér. Théor. Approx., 41(2), 114–124. https://doi.org/10.33993/jnaat412-973

Issue

Vol. 41 No. 2 (2012)

Section

Articles

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

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