Research Article

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

Volume: 2 Number: 3 September 1, 2019
EN

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

Abstract

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

Keywords

References

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

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

September 1, 2019

Submission Date

April 13, 2019

Acceptance Date

July 11, 2019

Published in Issue

Year 2019 Volume: 2 Number: 3

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

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