论文信息 - Pointwise Approximation Theorems for Combinations and Derivatives of Bernstein Polynomials

Pointwise Approximation Theorems for Combinations and Derivatives of Bernstein Polynomials

AbstractWe establish the pointwise approximation theorems for the combinations of Bernstein polynomials by the rth Ditzian–Totik modulus of smoothness $$ \omega ^{r}_{\Phi } (f,t) $$where Φ is an admissible step–weight function. An equivalence relation between the derivatives of these polynomials and the smoothness of functions is also obtained.

Linsen Xie | Lin Sen Xie

[1] George G. Lorentz,et al. Inverse Theorems for Bernstein Polynomials , 1997 .

[2] I. P. Natanson. Constructive function theory , 1964 .

[3] Ding-Xuan Zhou,et al. On Smoothness Characterized by Bernstein Type Operators , 1995 .

[4] Zeev Ditzian,et al. Bernstein-type operators and their derivatives , 1989 .

[5] Direct and Inverse Estimates for Bernstein Polynomials , 1998 .

[6] V. Totik,et al. Moduli of smoothness , 1987 .

[7] Z. Ditzian. Derivatives of Bernstein polynomials and smoothness , 1985 .

[8] Z. Ditzian,et al. Direct estimate for Bernstein polynomials , 1994 .

[9] P. Butzer. Linear Combinations of Bernstein Polynomials , 1953, Canadian Journal of Mathematics.

[10] Z. Ditzian,et al. A global inverse theorem for combinations of Bernstein polynomials , 1979 .

[11] G. Alexits. Approximation theory , 1983 .