On an operator of Stancu-type with fixed points e_1 and e_2
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Abstract
The objective of this paper is to introduce an operator of Stancu-type, with the properties that the test functions $e_1$ and $e_2$ are reproduced. Also, in our approach, a theorem of error approximation and a Voronovskaja-type theorem for this operator are obtained.
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Indrea, A.
(2015).
On an operator of Stancu-type with fixed points e_1 and e_2.
Acta Mathematica Universitatis Comenianae, 84(1), 123-131.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/84/131
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References
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[3] Braica, P.I., Pop, O.T., Barbosu, D. and Piscoran, L., About a linear and positive operator of Stancu-type with xed points e0 and e1 (submitted)
[4] Braica, P.I., Pop, O.T. and Indrea, A.D., About a King-type operator, Appl. Math. Inf. Sci, No. 6 (1)(2012), 191-197
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[6] Indrea, A.D., A particular class of linear and positive Stancu-type operators, Acta Univ. Apulensis, No. 31(2012), 249-256
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[10] Pop, O.T., Indrea, A.D. and Braica, P.I., Durrmeyer operators of King-type, Annals of the University of Craiova, Math.Comp.Sci.Ser. 39(2), (2012), 288-298
[11] Stancu, D.D., On a generalization of the Bernstein polynomials, Studia Univ. "Babes - Bolyai", Scr. Math - Phis 14, (1969), 31-45 (in Romanian)
[2] Barbosu, D., Introduction in numerical analysis and approximation theory, Ed. Univ. de Nord Baia Mare, 2009.
[3] Braica, P.I., Pop, O.T., Barbosu, D. and Piscoran, L., About a linear and positive operator of Stancu-type with xed points e0 and e1 (submitted)
[4] Braica, P.I., Pop, O.T. and Indrea, A.D., About a King-type operator, Appl. Math. Inf. Sci, No. 6 (1)(2012), 191-197
[5] Gadjiev, A.D., Ghobanalizadeh, A.M., Approximation properties of a new type Berstein-Stancu polynomials of one and two variables, Appl. Math. Comp., (2010), No. 216, 890-901
[6] Indrea, A.D., A particular class of linear and positive Stancu-type operators, Acta Univ. Apulensis, No. 31(2012), 249-256
[7] King, J. P., Positive linear operators which preserve x^2, Acta Math. Hungar., 99 (2003), No. 3, 203-208
[8] Oancea, Ingrid A., Berstein - Stancu type operator wich preserves e2, An. St. Univ. Ovidius Constanta, Vol. 17(1) (2009), 145-152
[9] Pop, O. T., The generalization of Voronovskaja's theorem for a class of liniar and positive operators, Rev. Anal. Numer. Theor. Approx., 34 (2005), No. 1, 79-91
[10] Pop, O.T., Indrea, A.D. and Braica, P.I., Durrmeyer operators of King-type, Annals of the University of Craiova, Math.Comp.Sci.Ser. 39(2), (2012), 288-298
[11] Stancu, D.D., On a generalization of the Bernstein polynomials, Studia Univ. "Babes - Bolyai", Scr. Math - Phis 14, (1969), 31-45 (in Romanian)