Parametric Representation of Univalent Functions with Boundary Regular Fixed Points

Fixed Points of Univalent Functions Ii

For a closed nowhere dense subset C of ∂D a bounded univalent holomorphic function f on D is found such that C equals the cluster set of its fixed points.

Convexity of a family of meromorphically univalent functions by using two fixed points

In this paper a new class of meromorphic univalent functions in terms of an integral operator F c (z) = 1 0 cv c f (vz)dv, (c ≥ 1), is defined. We fined some properties of this new class by using of two fixed points.

Regular Points of Lipschttz Functions

Let/be a locally Lipschitz function on a Banach space X, and S a subset of X. We define regular (i.e. noncritical) points for / relative to S, and give a sufficient condition for a point z e S to be regular. This condition is then expressed in the particular case when/is C1, and is used to obtain a new proof of Hoffman's inequality in linear programming.

Univalent Functions with Univalent Derivatives. Ii

Univalent holomorphic functions with fixed finitely many coefficients involving Salagean operator

By using generalized Salagean differential operator a newclass of univalent holomorphic functions with fixed finitely manycoefficients is defined. Coefficient estimates, extreme points,arithmetic mean, and weighted mean properties are investigated.