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On the Iterates of Jackson Type Operator \({G_{s,n}}\)

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Abstract

In this paper, we study the limit of the iterates of a large class of linear bounded operators preserving constants. We obtain in addition the limit of the iterates of algebraic version of the trigonometric Jackson integrals. The proofs are based on spectral theory of linear operators.

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References

  1. Altomare, F.: On some convergence criteria for nets of positive operators on continuous function spaces. J. Math. Anal. Appl. 398, 542–552 (2013)

  2. Badea C.: Bernstein polynomials and operator theory. Results Math. 53(3–4), 229–236 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cao J., Gonska H.: Approximation by Boolean sums of positive linear operators III: estimates for some numerical approximation schemes. Numer. Funct. Anal. Optim. 10(7, 8), 643–672 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. DeVore R., Lorentz G.: Constructive Approximation. Springer, Berlin (1993)

    Book  MATH  Google Scholar 

  5. Gavrea I., Ivan M.: On the iterates of positive linear operators preserving the affine functions. J. Math. Anal. Appl. 372(2), 366–368 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gavrea, I., Ivan, M.: Asymptotic behaviour of the iterates of positive linear operators. Abstr. Appl. Anal. 2011, 1–11 (2011)

  7. Gavrea I., Ivan M.: The iterates of positive linear operators preserving constants. Appl. Math. Lett. 24(12), 2068–2071 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gavrea I., Ivan M.: The iterates of positive linear operators preserving constants. Appl. Math. Lett. 24(12), 2068–2071 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Nagler J.: On the spectrum of positive linear operators with partition of unity property. J. Math. Anal. Appl. 425, 249–258 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Nagler J., Cerejeiras P., Forster B.: Lower bounds for approximation with variation-diminishing splines. J. Complex. 32, 1–11 (2015)

    MathSciNet  MATH  Google Scholar 

  11. Rudin, W.: (1991) Functional Analysis, 2nd ed. McGraw-Hill, Inc., New York

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Authors and Affiliations

  1. Department of Applied Mathematics, Varna University of Economics, Varna, Bulgaria

    T. Zapryanova & D. Souroujon

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  1. T. Zapryanova
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  2. D. Souroujon
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Correspondence to D. Souroujon.

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Zapryanova, T., Souroujon, D. On the Iterates of Jackson Type Operator \({G_{s,n}}\) . Mediterr. J. Math. 13, 5053–5061 (2016). https://doi.org/10.1007/s00009-016-0791-8

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  • DOI: https://doi.org/10.1007/s00009-016-0791-8

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