We begin by classifying all solutions of two natural recurrences that Bernstein polynomials satisfy. The first scheme gives a natural characterization of Stancu polynomials. In Section 2, we identify the Bernstein polynomials as coefficients in the generating function for the elementary symmetric fu
Convergence of Generalized Bernstein Polynomials
β Scribed by Alexander Il'inskii; Sofiya Ostrovska
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 120 KB
- Volume
- 116
- Category
- Article
- ISSN
- 0021-9045
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π SIMILAR VOLUMES
We give an interesting generalization of the Bernstein polynomials. We find sufficient and necessary conditions for uniform convergence by the new polynomials, and we generalize the Bernstein theorem.
Weighted mean convergence of generalized Jacobi series is investigated, and the results are used to prove weighted mean convergence of various interpolating polynomials based on the zeros of generalized Jacobi polynomials. C 1993 Academic Press. Inc.
Weighted mean convergence of interpolating polynomials based on the zeros of generalized Jacobi polynomials is investigated. The approach is based on generalized Jacobi series and Marcinkiewicz-Zygmund type inequality. 1994 Academic Press. Inc.