Approximation and geometric properties of some complex Bernstein-Stancu polynomials in compact disks

Authors

  • Sorin G. Gal University of Oradea, Romania

DOI:

https://doi.org/10.33993/jnaat361-856

Keywords:

complex Bernstein-Stancu polynomials, simultaneous approximation, iterates of complex Bernstein-Stancu polynomials, shape preserving properties, univalent, starlike, convex and spirallike function
Abstract views: 228

Abstract

In this paper, the order of simultaneous approximation, convergence results of the iterates and shape preserving properties, for complex Bernstein-Stancu polynomials (depending on one parameter) attached to analytic functions on compact disks are obtained.

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References

Agratini, O. and Rus, I.A., Iterates of some bivariate approximation process via weakly Picard operators, Nonlinear Anal. Forum, 8, no. 2, pp. 159-168, 2003.

Gal, S.G., Shape Preserving Approximation by Real and Complex Polynomials, Birkhauser Publ., Boston, under press, https://doi.org/10.1007/978-0-8176-4703-2 DOI: https://doi.org/10.1007/978-0-8176-4703-2

Gal, S.G., Voronovskaja's theorem and iterations for complex Bernstein polynomials in compact disks, submitted., https://doi.org/10.1007/s00009-008-0148-z DOI: https://doi.org/10.1007/s00009-008-0148-z

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Gonska, H., Piţul, P. and Raşa, I., Over-iterates of Bernstein-Stancu operators, Calcolo, 44, no. 2, pp. 117-125, 2007, https://doi.org/10.1007/s10092-007-0131-2 DOI: https://doi.org/10.1007/s10092-007-0131-2

Lorentz, G.G., Bernstein Polynomials, 2nd edition, Chelsea Publ., New York, 1986.

Mocanu, P.T., Bulboacă T. and Sălăgean, Gr. St., Geometric Function Theory of Univalent Functions (in Romanian), Science Book' s House, Cluj-Napoca, 1999.

Stancu, D.D., Approximation of functions by a new class of linear polynomial operators, Rev. Roumaine. Math. Pures Appl., 13, pp. 1173-1194, 1968.

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Published

2007-02-01

How to Cite

Gal, S. G. (2007). Approximation and geometric properties of some complex Bernstein-Stancu polynomials in compact disks. Rev. Anal. Numér. Théor. Approx., 36(1), 67–77. https://doi.org/10.33993/jnaat361-856

Issue

Vol. 36 No. 1 (2007)

Section

Articles

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

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