共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove that an absolute constantc>0 exists such that
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2.
We define generalized polynomials as products of polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We prove Markov-, Bernstein-, and Remez-type inequalities inL
p
(0p) and Nikolskii-type inequalities for such generalized polynomials. Our results extend the corresponding inequalities for ordinary polynomials.Communicated by George G. Lorentz. 相似文献
3.
F. Peherstorfer 《Constructive Approximation》1997,13(2):261-269
We give explicitly a class of polynomials with complex coefficients of degreen which deviate least from zero on [−1, 1] with respect to the max-norm among all polynomials which have the same,m + 1, 2m ≤n, first leading coefficients. Form=1, we obtain the polynomials discovered by Freund and Ruschewyh. Furthermore, corresponding results are obtained with respect
to weight functions of the type 1/√ρl, whereρl is a polynomial positive on [−1, 1]. 相似文献
4.
T. Erdèlyi 《Constructive Approximation》1989,5(1):347-356
Establishing Markov-type inequalities for the derivatives of polynomials with restricted zeros was initiated by P. Erdös [3] in 1940. Since then several authors proved similar estimates for the derivatives of polynomials of special type. In this paper we work on [–1, 1] and obtain Markov-type estimates for the derivatives of polynomials from a rather wide family of classes of constrained polynomials. In some cases the results turn out to be sharp.Communicated by George G. Lorentz. 相似文献
5.
Erich van Wickeren 《Constructive Approximation》1989,5(1):189-198
Equivalence theorems concerning the convergence of the Bernstein polynomialsB
n
f are well known for continuous functionsf in the sup-norm. The purpose of this paper is to extend these results for functionsf, Riemann integrable on [0, 1], We have therefore to consider the seminorm
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