# Approximation by Faber-Laurent Rational Functions on Doubly Connected Domains

### New Zealand Journal of Mathematics

Vol. 44, (2014), Pages 113-124

Hasan Yurt

Department of Mathematics,

Faculty of Arts and Sciences,

Canakkale Onsekiz Mart University,

17020 Canakkale, Turkey.

Ali Guven

Department of Mathematics,

Faculty of Arts and Sciences,

Balikesir University,

10145 Balikesir, Turkey.

Abstract Let B be a doubly-connected domain bounded by two Dini-smooth curves. In this work, we prove some direct theorems of approximation theory in weighted rearrangement invariant Smirnov spaces $E_{X}\left( B,\omega \right)$ defined on B. For this, approximation properties of the Faber-Laurent rational series expansions are used.

Keywords Cauchy singular operator, Faber-Laurent rational function, Muckenhoupt weight, weighted rearrangement invariant space.

Classification (MSC2000) 30E10, 41A20, 41A25, 46E30.