Research Article

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

Volume: 3 Number: 1 May 15, 2015
EN

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

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

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  4. [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. [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. [6] Stancu, D.D. Approximation of functions by means of a new generalized Bernstein operator, Calcolo 20 211–229, 1983.
  7. [7] Shiryayev, A.N. Probability. Springer-Verlag, New York, 1984.
  8. [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. [9] Zeng X.-M., Bounds for Bernstein basis functions and Meyer-K¨onig-Zeller basis functions, J. Math. Anal. Appl. 219:364-376, 1998.
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
1.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):126-136. doi:10.36753/mathenot.421231
Chicago
Uster, Rüya, and Ertan İbikli. 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): 126-36. 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
[1]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, May 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 1, 2015): 126-136. https://doi.org/10.36753/mathenot.421231.
JAMA
1.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, May 2015, pp. 126-3, doi:10.36753/mathenot.421231.
Vancouver
1.Rüya Uster, Ertan İbikli. ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION. Math. Sci. Appl. E-Notes. 2015 May 1;3(1):126-3. doi:10.36753/mathenot.421231