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

### From NZJM

**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 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.