Sentence examples for maps the disk from inspiring English sources

If, then the function maps the disk onto a domain starlike with respect to the origin.

If, then a function maps the disk onto a domain starlike with respect to the origin.

A function maps the disk,, onto a domain starlike with respect to theorigin if and only if (7).

and every function maps the disk onto a domain starlike with respect to the origin.The set is called the set of generalized starlikeness of theclass ℋ.

where w ( z ) is analytic and | w ( z ) | ≤ | z | in U. Noting that h ( z ) maps the disk | z | < ρ ( 0 < ρ ≤ 1 ) onto a region which is convex and symmetric with respect to the real axis, we know that h ( − ρ | z | ) ≤ ℜ { h ( ρ w ( z ) ) } ≤ h ( ρ | z | ) ( z ∈ U ). (2.10).

The automorphisms of (mathbb{D}), that is, the one-to-one analytic maps of the disk onto itself, are just the functions (varphi z)=lambdafrac{a-z}{1-overline{a}z}) with (|lambda|=1) and (|a| < 1).

Let f be an holomorphic function which maps the unit disk into itself.

where is an analytic function with positive real part,, and maps the unit disk onto a region starlike with respect to 1.

The Koebe function is univalent and starlike in D and maps the unit disk D onto the complex plane minus a slit ( − ∞, − 1 4 ]. Several generalizations of k 2 appeared in the literature. Robertson [1] proved that k 2 ( 1 − α ) ( z ) = z ( 1 − z ) 2 ( 1 − α ) ( 0 ≤ α < 1 ) is the extremal function for the class of functions starlike of order α.

To this end, we compose three well-known conformal mappings: 1. η = 1 ı ζ + 1 ζ - 1 Open image in new window maps the unit disk D Open image in new window conformally onto the upper half-plane H : = { η ∈ C : J η > 0 } Open image in new window.

Letφbe an analytic map of the disk into itself (that fixes the origin).