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A Quantitative Variant of Voronovskaja's Theorem for King-Type Operators

Year 2019, , 124 - 129, 01.09.2019
https://doi.org/10.33205/cma.553427

Abstract

In this note we establish a quantitative Voronovskaja theorem for modified Bernstein polynomials using the first order Ditzian-Totik modulus  of smoothness.

References

  • [1] J. M. Aldaz, O. Kounchev and H. Render: Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces. Numer. Math. 114 (2009), 1–25.
  • [2] Z. Ditzian and V. Totik: Moduli of Smoothness. Springer, New York, 1987.
  • [3] Z. Finta: On generalized Voronovskaja theorem for Bernstein polynomials. Carpathian J. Math. 28 (2012), 231–238.
  • [4] M. S. Floater: On the convergence of derivatives of Bernstein approximation. J. Approx. Theory. 134 (2005), 130–135.
  • [5] H. Gonska and I. Ras ̧a: Asymptotic behavior of differentiated Bernstein polynomials. Math. Vesnik. 61 (2009), 53–60.
  • [6] H. Gonska and G. Tachev: A quantitative variant of Voronovskaja’s theorem. Result. Math. 53 (2009), 287–294.
  • [7] H. Gonska, M. Heilmann and I. Raşa: Asymptotic behavior of differentiated Bernstein polynomials revisited. General Math. 18 (2010), 45–53.
  • [8] J. P. King: Positive linear operators which preserve x2. Acta Math. Hungar. 99 (2003), 203–208.
Year 2019, , 124 - 129, 01.09.2019
https://doi.org/10.33205/cma.553427

Abstract

References

  • [1] J. M. Aldaz, O. Kounchev and H. Render: Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces. Numer. Math. 114 (2009), 1–25.
  • [2] Z. Ditzian and V. Totik: Moduli of Smoothness. Springer, New York, 1987.
  • [3] Z. Finta: On generalized Voronovskaja theorem for Bernstein polynomials. Carpathian J. Math. 28 (2012), 231–238.
  • [4] M. S. Floater: On the convergence of derivatives of Bernstein approximation. J. Approx. Theory. 134 (2005), 130–135.
  • [5] H. Gonska and I. Ras ̧a: Asymptotic behavior of differentiated Bernstein polynomials. Math. Vesnik. 61 (2009), 53–60.
  • [6] H. Gonska and G. Tachev: A quantitative variant of Voronovskaja’s theorem. Result. Math. 53 (2009), 287–294.
  • [7] H. Gonska, M. Heilmann and I. Raşa: Asymptotic behavior of differentiated Bernstein polynomials revisited. General Math. 18 (2010), 45–53.
  • [8] J. P. King: Positive linear operators which preserve x2. Acta Math. Hungar. 99 (2003), 203–208.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Zoltán Fınta 0000-0003-2104-3483

Publication Date September 1, 2019
Published in Issue Year 2019

Cite

APA Fınta, Z. (2019). A Quantitative Variant of Voronovskaja’s Theorem for King-Type Operators. Constructive Mathematical Analysis, 2(3), 124-129. https://doi.org/10.33205/cma.553427
AMA Fınta Z. A Quantitative Variant of Voronovskaja’s Theorem for King-Type Operators. CMA. September 2019;2(3):124-129. doi:10.33205/cma.553427
Chicago Fınta, Zoltán. “A Quantitative Variant of Voronovskaja’s Theorem for King-Type Operators”. Constructive Mathematical Analysis 2, no. 3 (September 2019): 124-29. https://doi.org/10.33205/cma.553427.
EndNote Fınta Z (September 1, 2019) A Quantitative Variant of Voronovskaja’s Theorem for King-Type Operators. Constructive Mathematical Analysis 2 3 124–129.
IEEE Z. Fınta, “A Quantitative Variant of Voronovskaja’s Theorem for King-Type Operators”, CMA, vol. 2, no. 3, pp. 124–129, 2019, doi: 10.33205/cma.553427.
ISNAD Fınta, Zoltán. “A Quantitative Variant of Voronovskaja’s Theorem for King-Type Operators”. Constructive Mathematical Analysis 2/3 (September 2019), 124-129. https://doi.org/10.33205/cma.553427.
JAMA Fınta Z. A Quantitative Variant of Voronovskaja’s Theorem for King-Type Operators. CMA. 2019;2:124–129.
MLA Fınta, Zoltán. “A Quantitative Variant of Voronovskaja’s Theorem for King-Type Operators”. Constructive Mathematical Analysis, vol. 2, no. 3, 2019, pp. 124-9, doi:10.33205/cma.553427.
Vancouver Fınta Z. A Quantitative Variant of Voronovskaja’s Theorem for King-Type Operators. CMA. 2019;2(3):124-9.