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Approximation of Functions by Means of Some New Classes of Positive Linear Operators

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Numerische Methoden der Approximationstheorie

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

  1. 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.

    Google Scholar 

  2. Cheney, E. W.: Introduction to Approximation Theory. New York, 1966.

    Google Scholar 

  3. Lorentz, G. G.: Bernstein Polynomials. Toronto, 1953.

    Google Scholar 

  4. Lorentz, G. G.: Approximation of Functions. New York, 1966.

    Google Scholar 

  5. Lupas, A.: Some properties of the linear positive operators (II). Mather matica (Cluj), 9(32) (1967), 295–298.

    Google Scholar 

  6. Mamedov, R. G.: On the order of approximation of functions by linear positive operators. Dokl. Akad. Nauk SSSR, 128 (1959), 674–676.

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  7. Schurer, F.: On linear positive operators in approximation theory. Doct. thesis, Delft, 1965.

    Google Scholar 

  8. Shisha, O. and B. Mond: The degree of convergence of sequences of linear positive operators. Proc. Nat. Acad. Sei. USA, 60 (1968), 1196–1200.

    Article  Google Scholar 

  9. Sikkema, P. C.: On some research in linear positive operators in approximation theory. Nieuw Arch. Wisk., 18 (1970), 36–60.

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  10. Stancu, D. D.: Approximation of functions by a new class of linear polynomial operators. Rev. Roumaine Math. Pures Appl., 13(1968), 1173–1194.

    Google Scholar 

  11. Stancu, D. D.: On a new positive linear polynomial operator. Proc. Japan Acad., 44 (1968), 221p–224.

    Article  Google Scholar 

  12. 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.

    Google Scholar 

  13. Stancu, D. D.: On a generalization of the Bernstein polynomials. Studia Univ. Babes-Bolyai, Cluj, 14(1969), 31–45.

    Google Scholar 

  14. Stancu, D. D.: Approximation properties of a class of linear positive operators. Ibid., 15 (1970), 31–38.

    Google Scholar 

  15. Stancu, D. D.: Two classes of positive linear operators. Analele Univ. Timisoara, 8 (1970).

    Google Scholar 

  16. 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.

    Google Scholar 

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© 1972 Springer Basel AG

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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

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5953-0

  • Online ISBN: 978-3-0348-5952-3

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