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Asymptotic distribution of poles and zeros of best rational approximants to $x^α$ on [0,1]

100%

Saff E. B. , Stahl H.

nr 1

329-348

Let $r_n* ∈ ℛ_{nn}$ be the best rational approximant to $f(x) = x^α$, 1 > α > 0, on [0,1] in the uniform norm. It is well known that all poles and zeros of $r_n*$ lie on the negative axis $ℝ_{<0}$. In the present paper we investigate the asymptotic distribution of these poles and zeros as n → ∞. In addition we determine the asymptotic distribution of the extreme points of the error function $e_n = f - r_n*$ on [0,1], and survey related convergence results.

On some means of double Fourier series

75%

Taberski R.

tom [Z] 38

139-148

For bivariate periodic functions Lebesgue-integrable on the basic square and corresponding p>0, the rates of Lp - convergence of the means (1), (3) are estimated. The one-dimensional case was considered in Sections 3, 4 of [6].

Best approximation and fixed points for rational-type contraction mappings

63%

Chandok S.

tom Vol. 25, nr 2

205--209

In this paper, we prove a fixed point theorem for a rational type contraction mapping in the frame work of metric spaces. Also, we extend Brosowski-Meinardus type results on invariant approximation for such class of contraction mappings. The results proved extend some of the known results existing in the literature.