A criterion for normality of analytic mappings

Univalence Criterion for Analytic Functions

In this paper, we obtain a new univalence criterion for analytic functions defined outside of the unit disk. Relevant connections of the results, which are presented in this paper with various known results are also considered. 2000 Mathematics Subject Classification: Primary 30C45.

Normality of Composite Analytic Functions and Sharing an Analytic Function

A result of Hinchliffe 2003 is extended to transcendental entire function, and an alternative proof is given in this paper. Our main result is as follows: let α z be an analytic function, F a family of analytic functions in a domain D, and H z a transcendental entire function. If H ◦ f z and H ◦ g z share α z IM for each pair f z , g z ∈ F, and one of the following conditions holds: 1 H z −α z0...

On the Normality of an Analytic Operator1

Complex Analytic Mappings

The Convenient Setting for Real Analytic Mappings

We present here ”the” cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps smooth curves to smooth curves and real analytic curves to real analytic curves. Under mild completeness conditions the second requirement can be replaced by: real analytic along affine lines. Enclose...