Abstract
The purpose of this paper is to introduce some new classes of positive linear operators, depending on some real parameters, and to examine their main approximation properties to real-valued functions. These operators generalize the well-known operators of Bernstein, Baskakov, Favard-Szasz, etc.
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References
Baskakov, V. A.: An example of a sequence of linear positive operators in the space of continuous functions. Dokl. Akad. Nauk SSSR, 113 (1957), 249–251.
Cheney, E. W.: Introduction to Approximation Theory. New York, 1966.
Lorentz, G. G.: Bernstein Polynomials. Toronto, 1953.
Lorentz, G. G.: Approximation of Functions. New York, 1966.
Lupas, A.: Some properties of the linear positive operators (II). Mather matica (Cluj), 9(32) (1967), 295–298.
Mamedov, R. G.: On the order of approximation of functions by linear positive operators. Dokl. Akad. Nauk SSSR, 128 (1959), 674–676.
Schurer, F.: On linear positive operators in approximation theory. Doct. thesis, Delft, 1965.
Shisha, O. and B. Mond: The degree of convergence of sequences of linear positive operators. Proc. Nat. Acad. Sei. USA, 60 (1968), 1196–1200.
Sikkema, P. C.: On some research in linear positive operators in approximation theory. Nieuw Arch. Wisk., 18 (1970), 36–60.
Stancu, D. D.: Approximation of functions by a new class of linear polynomial operators. Rev. Roumaine Math. Pures Appl., 13(1968), 1173–1194.
Stancu, D. D.: On a new positive linear polynomial operator. Proc. Japan Acad., 44 (1968), 221p–224.
Stancu, D. D.: Use of probabilistic methods in the theory of uniform approximation of continuous functions. Rev. Roumaine Math. Pures Appl., 14 (1969), 673–691.
Stancu, D. D.: On a generalization of the Bernstein polynomials. Studia Univ. Babes-Bolyai, Cluj, 14(1969), 31–45.
Stancu, D. D.: Approximation properties of a class of linear positive operators. Ibid., 15 (1970), 31–38.
Stancu, D. D.: Two classes of positive linear operators. Analele Univ. Timisoara, 8 (1970).
Stancu, D. D.: On the remainder of approximation of functions by means of a parameter-dependent linear polynomial operator. Studia Univ. Babes-Bolyai, Cluj, 16 (1971), 59–66.
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Stancu, D.D. (1972). Approximation of Functions by Means of Some New Classes of Positive Linear Operators. In: Collatz, L., Meinardus, G. (eds) Numerische Methoden der Approximationstheorie. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 16. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5952-3_17
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DOI: https://doi.org/10.1007/978-3-0348-5952-3_17
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