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Approximation of Analytic Functions by Generalized Favard–Szász–Mirakjan–Faber Operators in Compact Sets

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Abstract

Let \(a_{n}>0, b_{n}>0, n\in \mathbb {N}\), be two sequences with the property that \(\frac{b_{n}}{a_{n}}\searrow 0\) as fast as we want. In this paper we construct a generalized Favard–Szász–Mirakjan–Faber operator attached to analytic functions of exponential growth in a continuum in \(\mathbb {C}\) , for which the approximation order \(\frac{b_{n}}{a_{n}}\) is obtained. Also, several concrete examples are presented.

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References

  1. Cetin, N., Ispir, N.: Approximation by complex modified Szász–Mirakjan operators. Studia Sci. Math. Hung. 50(3), 355–372 (2013)

    MATH  MathSciNet  Google Scholar 

  2. Dressel, F.G., Gergen, J.J., Purcell, W.H.: Convergence of extended Bernstein polynomials in the complex plane. Pac. J. Math. 13(4), 1171–1180 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  3. Gaier, D.: Lectures on Complex Approximation. Birkhauser, Boston (1987)

    Book  MATH  Google Scholar 

  4. Gal, S.G.: Approximation by Complex Bernstein and Convolution-Type Operators. World Scientific Publ. Co, Singapore (2009)

    MATH  Google Scholar 

  5. Gal, S.G.: Approximation and geometric properties of complex Favard–Szász–Mirakjan operators in compact diks. Comput. Math. Appl. 56, 1121–1127 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gal, S.G.: Overconvergence in Complex Approximation. Springer, New York (2013)

    Book  MATH  Google Scholar 

  7. Gal, S.G.: Voronovskaja-type results in compact disks for quaternion q-Bernstein operators, \(q\ge 1\). Complex Analysis and Operator Theory 6(2), 515–527 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gal, S.G., Mahmudov, N.I., Kara, M.: Approximation by complex \(q\)-Szász-Kantorovich operators in compact disks, \(q\) > 1. Complex Anal. Oper. Theory 7(6), 1853–1867 (2013)

  9. Gupta, V.: Approximation properties by Bernstein–Durrmeyer type operators. Complex Anal. Oper. Theory 7(2), 363–374 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  10. Popescu, D., Oboroceanu, G.: Exercises and Problems of Combinatorial Algebra and Number Theory (Romanian). In: Didact Pedag (ed.). Bucharest (1979)

  11. Suetin, P.K.: Series of Faber Polynomials. Gordon and Breach, Amsterdam (1998)

    MATH  Google Scholar 

  12. Szász, O.: Generalization of S. Bernstein’s polynomials to the infinite interval. J. Res. Natl. Bur. Stand. 45, 239–245 (1950)

    Article  Google Scholar 

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Acknowledgments

The author thanks the referee for his/her valuable comments.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Oradea, Str. Universitatii No. 1, 410087 , Oradea, Romania

    Sorin G. Gal

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  1. Sorin G. Gal
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Correspondence to Sorin G. Gal.

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Communicated by Daniel Aron Alpay.

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Gal, S.G. Approximation of Analytic Functions by Generalized Favard–Szász–Mirakjan–Faber Operators in Compact Sets. Complex Anal. Oper. Theory 9, 975–984 (2015). https://doi.org/10.1007/s11785-014-0383-1

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  • DOI: https://doi.org/10.1007/s11785-014-0383-1

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