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

Rüya Uster; Ertan İbikli

doi:10.36753/mathenot.421231

Research Article

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

Rüya Uster Ertan İbikli

https://doi.org/10.36753/mathenot.421231

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

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	Articles
Authors	Rüya Uster Ertan İbikli
Publication Date	May 15, 2015
Submission Date	October 15, 2014
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 (May 2015), 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.