𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Generalization of the Bernstein Polynomials

✍ Scribed by Jia-Ding Cao


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
136 KB
Volume
209
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis


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.


📜 SIMILAR VOLUMES


Generalized Bernstein Polynomials and Sy
✍ Robert P Boyer; Linda C Thiel 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 166 KB

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

A Generalization of Bernstein–Kantorovič
✍ Jesús de la Cal; Ana M Valle 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 125 KB

In this paper, we use a probabilistic setting to introduce a double sequence Ž ² k : . L of linear polynomial operators which includes, as particular cases, the n classical Bernstein operators, the Kantorovic operators, and the operators recently ǐntroduced by Cao. For these operators, we discuss se

Generalization of the Left Bernstein Qua
✍ Yasuo Kageyama 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 345 KB

P. SablonnieÁ re introduced the so-called left Bernstein quasi-interpolant, and proved that the sequence of the approximating polynomials converges pointwise in high-order rate to each sufficiently smooth approximated function. On the other hand, Z.-C. Wu proved that the sequence of the norms of the

Bernstein Polynomials and Modulus of Con
✍ Zhongkai Li 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 89 KB

p n, j (x)= \ n j + x j (1&x) n& j of a given function f (x) on [0, 1], besides the convergence and approximation, preserve some properties of the original function. For example: (i) if f (x) is non-decreasing, then for all n 1, the B n ( f; x) are nondecreasing; (ii) if f (x) is convex, then for