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On differences of linear positive operators

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Abstract

In this paper we consider two different general linear positive operators defined on unbounded interval and obtain estimates for the differences of these operators in quantitative form. Our estimates involve an appropriate K-functional and a weighted modulus of smoothness. Similar estimates are obtained for Chebyshev functional of these operators as well. All considerations are based on rearrangement of the remainder in Taylor’s formula. The obtained results are applied for some well known linear positive operators.

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References

  1. Acu, A.M., Raşa, I.: New estimates for the differences of positive linear operators. Numer. Algorithms 73, 775–789 (2016)

    Article  MathSciNet  Google Scholar 

  2. Agratini, O.: Properties of discrete non-multiplicative operators. Anal. Math. Phys. (2017). https://doi.org/10.1007/s13324-017-0186-4

    Article  MATH  Google Scholar 

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

    Book  Google Scholar 

  4. Gonska, H., Pitul, P., Raşa, I.: On Peano’s form of the Taylor remainder, Voronovskaja’s theorem and the commutator of positive linear operators. In: Agratini, O., Blaga, P. (eds.) Proceedings of the International Conference on Numerical Analysis and Approximation Theory, Cluj-Napoca, 2006, pp. 55–80. Cluj-Napoca, Casa Cartii de Ştiinta (2006)

  5. Gonska, H., Pitul, P., Raşa, I.: On differences of positive linear operators. Carpathian J. Math. 22(1–2), 65–78 (2006)

    MathSciNet  MATH  Google Scholar 

  6. Gonska, H., Raşa, I.: Differences of positive linear operators and the second order modulus. Carpathian J. Math. 24(3), 332–340 (2008)

    MATH  Google Scholar 

  7. Ispir, N.: On modified Baskakov operators on weighted spaces. Turk. J. Math. 26(3), 355–365 (2001)

    MathSciNet  MATH  Google Scholar 

  8. Mazhar, S.M., Totik, V.: Approximation by modified Szász operators. Acta Sci. Math. 49, 257–269 (1985)

    MathSciNet  MATH  Google Scholar 

  9. Raşa, I., Stanilă, E.: On some operators linking the Bernstein and the genuine Bernstein–Durrmeyer operators. J. Appl. Funct. Anal. 9(3–4), 369–378 (2014)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Kırıkkale University, 71450, Yahşihan, Kırıkkale, Turkey

    Ali Aral

  2. Department of Mathematics, Technical University of Cluj-Napoca, Cluj, Romania

    Daniela Inoan & Ioan Raşa

Authors
  1. Ali Aral
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  2. Daniela Inoan
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  3. Ioan Raşa
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Correspondence to Ali Aral.

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Aral, A., Inoan, D. & Raşa, I. On differences of linear positive operators. Anal.Math.Phys. 9, 1227–1239 (2019). https://doi.org/10.1007/s13324-018-0227-7

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  • DOI: https://doi.org/10.1007/s13324-018-0227-7

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