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Year 2015, Volume: 3 Issue: 1, 126 - 136, 15.05.2015

Rüya Uster , Ertan İbikli

https://doi.org/10.36753/mathenot.421231
Cited By: 1

Abstract

References

  • [1] Bojanic, R. and Vuilleumier, M. On the rate of convergence of Fourier-Legendre series of functions of bounded variation, 1981.
  • [2] Cheng, F. On the rate of convergence of Bernstein polynomials of functions of bounded variation, 1983.
  • [3] Zeng. X. M. and Chen, W. On the rate of convergence of the generalized Durrmeyer type operators for functions of bounded variation. J. Approx. Theory 102:1-12, 2000.
  • [4] Guo, S. S. On the rate of convergence of Durrmeyer operator for functions of bounded variation. Journal of Approximation Theory 51, 183-197, 1987.
  • [5] Bernstein, S. N. Demonstration du Th´eoreme de Weierstrass fond´eee sur le calcul des probabilit´es. Comm. Soc. Math. 13:1-2, 1912.
  • [6] Stancu, D.D. Approximation of functions by means of a new generalized Bernstein operator, Calcolo 20 211–229, 1983.
  • [7] Shiryayev, A.N. Probability. Springer-Verlag, New York, 1984.
  • [8] Karsli, H. and Ibikli, E. Rate of Convergence of Chlodowsky-Type Bernstein Operators for Functions of Bounded Variation, Numerical Functional Analysis and Optimization, 28:3-4, 367-378, 2007.
  • [9] Zeng X.-M., Bounds for Bernstein basis functions and Meyer-K¨onig-Zeller basis functions, J. Math. Anal. Appl. 219:364-376, 1998.

ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION

Year 2015, Volume: 3 Issue: 1, 126 - 136, 15.05.2015

Rüya Uster , Ertan İbikli

https://doi.org/10.36753/mathenot.421231
Cited By: 1

Abstract

In this paper, we estimate the rate of pointwise convergence of the
Stancu type Bernstein operators for functions defined on the interval. To prove
our main result, we have used some methods and techniques from probability
theory.

Keywords

Approximation Bernstein-Stancu polynomials Bounded variation Total variation Rate of convergence

References

  • [1] Bojanic, R. and Vuilleumier, M. On the rate of convergence of Fourier-Legendre series of functions of bounded variation, 1981.
  • [2] Cheng, F. On the rate of convergence of Bernstein polynomials of functions of bounded variation, 1983.
  • [3] Zeng. X. M. and Chen, W. On the rate of convergence of the generalized Durrmeyer type operators for functions of bounded variation. J. Approx. Theory 102:1-12, 2000.
  • [4] Guo, S. S. On the rate of convergence of Durrmeyer operator for functions of bounded variation. Journal of Approximation Theory 51, 183-197, 1987.
  • [5] Bernstein, S. N. Demonstration du Th´eoreme de Weierstrass fond´eee sur le calcul des probabilit´es. Comm. Soc. Math. 13:1-2, 1912.
  • [6] Stancu, D.D. Approximation of functions by means of a new generalized Bernstein operator, Calcolo 20 211–229, 1983.
  • [7] Shiryayev, A.N. Probability. Springer-Verlag, New York, 1984.
  • [8] Karsli, H. and Ibikli, E. Rate of Convergence of Chlodowsky-Type Bernstein Operators for Functions of Bounded Variation, Numerical Functional Analysis and Optimization, 28:3-4, 367-378, 2007.
  • [9] Zeng X.-M., Bounds for Bernstein basis functions and Meyer-K¨onig-Zeller basis functions, J. Math. Anal. Appl. 219:364-376, 1998.
There are 9 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Rüya Uster

Ertan İbikli

Submission Date October 15, 2014
Publication Date May 15, 2015
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Uster, R., & İbikli, E. (2015). ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION. Mathematical Sciences and Applications E-Notes, 3(1), 126-136. https://doi.org/10.36753/mathenot.421231
AMA Uster R, İbikli E. ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION. Math. Sci. Appl. E-Notes. May 2015;3(1):126-136. doi:10.36753/mathenot.421231
Chicago Uster, Rüya, and Ertan İbikli. “ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION”. Mathematical Sciences and Applications E-Notes 3, no. 1 (May 2015): 126-36. https://doi.org/10.36753/mathenot.421231.
EndNote Uster R, İbikli E (May 1, 2015) ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION. Mathematical Sciences and Applications E-Notes 3 1 126–136.
IEEE R. Uster and E. İbikli, “ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION”, Math. Sci. Appl. E-Notes, vol. 3, no. 1, pp. 126–136, 2015, doi: 10.36753/mathenot.421231.
ISNAD Uster, Rüya - İbikli, Ertan. “ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION”. Mathematical Sciences and Applications E-Notes 3/1 (May2015), 126-136. https://doi.org/10.36753/mathenot.421231.
JAMA Uster R, İbikli E. ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION. Math. Sci. Appl. E-Notes. 2015;3:126–136.
MLA Uster, Rüya and Ertan İbikli. “ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 1, 2015, pp. 126-3, doi:10.36753/mathenot.421231.
Vancouver Uster R, İbikli E. ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION. Math. Sci. Appl. E-Notes. 2015;3(1):126-3.

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