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

Araştırma Makalesi

Yıl 2015, Cilt: 3 Sayı: 1, 126 - 136, 15.05.2015

Rüya Uster Ertan İbikli

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

Öz

Kaynakça

[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

Yıl 2015, Cilt: 3 Sayı: 1, 126 - 136, 15.05.2015

Rüya Uster Ertan İbikli

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

[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.

Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Articles
Yazarlar	Rüya Uster Ertan İbikli
Yayımlanma Tarihi	15 Mayıs 2015
Gönderilme Tarihi	15 Ekim 2014
Yayımlandığı Sayı	Yıl 2015 Cilt: 3 Sayı: 1

Kaynak Göster

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. Mayıs 2015;3(1):126-136. doi:10.36753/mathenot.421231
Chicago	Uster, Rüya, ve 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, sy. 1 (Mayıs 2015): 126-36. https://doi.org/10.36753/mathenot.421231.
EndNote	Uster R, İbikli E (01 Mayıs 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 ve E. İbikli, “ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION”, Math. Sci. Appl. E-Notes, c. 3, sy. 1, ss. 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 (Mayıs 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 ve Ertan İbikli. “ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION”. Mathematical Sciences and Applications E-Notes, c. 3, sy. 1, 2015, ss. 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.