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A Direct Theorem for MKZ-Kantorovich Operator

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Abstract

We characterize the approximation of functions in Lp norm by Kantorovich modification of the classical Meyer-König and Zeller operator. By defining an appropriate K-functional we prove a direct theorem for it.

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References

  1. V. A. Baskakov, An instance of a sequence of the linear positive operators in the space of continuous functions, Dokl. Akad. Nauk SSSR, 113 (1957), 249–251 (in Russian).

    MathSciNet  MATH  Google Scholar 

  2. L. Ahlfors, Complex Analysis, McGraw-Hill (New York, 1979).

    Google Scholar 

  3. M. Becker and R. J. Nessel, A global approximation theorem for Meyer-König and Zeller operators, Math. Z., 160 (1978), 195–206.

    Article  MathSciNet  MATH  Google Scholar 

  4. H. Berens and Y. Xu, On Bernstein–Durrmeyer polynomials with Jacobi weights, in: Approximation Theory and Functional Analysis (College Station, TX, 1990), Academic Press (Boston, MA, 1991), pp. 25–46.

    Google Scholar 

  5. W. Chen and Z. Ditzian, Strong converse inequality for Kantorovich polynomials, Constr. Approx., 10 (1994), 95–106.

    Article  MathSciNet  MATH  Google Scholar 

  6. Z. Ditzian and K. G. Ivanov, Strong converse inequalities, J. Anal. Math., 61 (1993) 61–111.

    Article  MathSciNet  MATH  Google Scholar 

  7. I. Gadjev, Strong converse result for uniform approximation by Meyer-König and Zeller operator, J. Math. Anal. Appl., 428 (2015), 32–42.

    Article  MathSciNet  MATH  Google Scholar 

  8. I. Gadjev, Approximation of functions by Baskakov–Kantorovich operator, Results Math., 70 (2016), 1443–1461.

    Article  MathSciNet  MATH  Google Scholar 

  9. H. H. Gonska and X. Zhou, The Strong converse inequality for Bernstein-Kantorovich operators, Comput. Math. Appl., 30 (1995), 103–128.

    Article  MathSciNet  MATH  Google Scholar 

  10. Sh. Guo, Q. Qi and C. Li, Strong converse inequalities for Meyer-König and Zeller operators, J. Math. Anal. Appl., 337 (2008), 994–1001.

    Article  MathSciNet  MATH  Google Scholar 

  11. L. Kantorovich, Sur certains développements suivant les polynômes de la forme de S. Bernstein, I, II, C. R. Acad. Sci. URSS, 20 (1930), 563–568, 595–600.

    MATH  Google Scholar 

  12. G. Lorentz, Bernstein Polynomials, Mathematical Expositions, no. 8, University of Toronto Press (Toronto, 1953).

    Google Scholar 

  13. W. Meyer-König and K. Zeller, Bernsteinsche Potenzreihen, Studia Math., 19 (1960), 89–94.

    Article  MathSciNet  MATH  Google Scholar 

  14. M. W. Müller, L p-approximation by the method of integral Meyer-König and Zeller operators, Studia Math., 63 (1978), 81–88.

    Article  MathSciNet  MATH  Google Scholar 

  15. V. Totik, Approximation by Meyer-König and Zeller type operators, Math. Z., 182 (1983), 425–446.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to I. Gadjev.

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This work was partially supported by grant DN 02/14 of the Fund for Scientific Research of the Bulgarian Ministry of Education and Science and by grant No. 80.10-120/2017 of the National Science Fund of the University of Sofia.

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Gadjev, I. A Direct Theorem for MKZ-Kantorovich Operator. Anal Math 45, 25–38 (2019). https://doi.org/10.1007/s10476-018-0636-8

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  • DOI: https://doi.org/10.1007/s10476-018-0636-8

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