ON THE RATE OF CONVERGENCE OF THE STANCU TYPE BERNSTEIN OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION
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,
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- [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.
- ISSN: 2147-6268
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2013
- Yayıncı: -