On typically real functions which are generated by a fixed typically real function

Title:

On typically real functions which are generated by a fixed typically real function

Creator:

Sobczak-Kneć, Magdalena and Trabka-Wiȩcław, Katarzyna

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a222979d-38f4-4d75-bcae-aea85ca25404
uuid:a222979d-38f4-4d75-bcae-aea85ca25404

Subject:

typically real functions, superdomain of local univalence, radius of local univalence, radius of starlikeness, and radius of univalence

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let ${\rm T}$ be the family of all typically real functions, i.e. functions that are analytic in the unit disk $\Delta :=\{ z \in \mathbb {C} \colon |z|<1 \}$, normalized by $f(0)=f'(0)-1=0$ and such that $\mathop {\rm Im} z \mathop {\rm Im} f(z) \geq 0$ for $z \in \Delta $. In this paper we discuss the class ${\rm T}_g$ defined as \[{\rm T}_g:= \{ \sqrt {f(z)g(z)} \colon f \in {\rm T} \},\quad g \in {\rm T}.\] We determine the sets $\bigcup _{g \in {\rm T}} {\rm T}_g$ and $\bigcap _{g \in {\rm T}} {\rm T}_g$. Moreover, for a fixed $g$, we determine the superdomain of local univalence of ${\rm T}_g$, the radii of local univalence, of starlikeness and of univalence of ${\rm T}_g$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

733-742

Source:

Czechoslovak Mathematical Journal | 2011 Volume:61 | Number:3

Harvested from:

CDK

Metadata only:

false