On close-to-star functions
Zaprawa, Paweł
Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, p. 469-480 / Harvested from Project Euclid
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For a given class $A$ and a set $D$ the sets $\bigcap_{f\in A}f(D)$ and $\bigcup_{f\in A}f(D)$ are called the Koebe set and the covering set for $A$ over $D$, respectively. These sets are found for the class $H$ of close-to-star functions $f$ of the form $f(z)=\frac{z}{1-z^2}p(z)$, where $Re p(z)>0, p(0)=1$. Analogous results concerning some other subclasses of close-to-star functions are established too.
Publié le : 2009-08-15
Classification:  close-to-star functions,  Koebe set,  covering set,  30C25,  30C45 
@article{1251832373,
     author = {Zaprawa, Pawe\l },
     title = {On close-to-star functions},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {16},
     number = {1},
     year = {2009},
     pages = { 469-480},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1251832373}
}

Zaprawa, Paweł. On close-to-star functions. Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, pp.  469-480. http://gdmltest.u-ga.fr/item/1251832373/