Functions typically-real and meromorphic in the unit circle

Cluster Sets of Functions Meromorphic in the Unit Circle.

Typically Real Harmonic Functions

We consider a class T O H of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some partial results about the region of univalence for this class.

Typically-real Functions with Assigned Zeros

is said to be typically-real of order p, if in (1.1) the coefficients bn are all real and if either (I) f(z) is regular in |a| =S1 and 3/(ei9) changes sign 2p times as z = eie traverses the boundary of the unit circle, or (II) f(z) is regular in | z\ < 1 and if there is a p < 1 such that for each r in p<r<l, $f(reie) changes sign 2p times as z = reie traverses the circle \z\ =r. This set of fun...

On the Derivatives of Functions Analytic in the Unit Circle.

Non-real Zeros of Derivatives of Real Meromorphic Functions

The main result of the paper determines all real meromorphic functions f of finite order in the plane such that f ′ has finitely many zeros while f and f(k), for some k ≥ 2, have finitely many non-real zeros. MSC 2000: 30D20, 30D35.