Geodesic
On the radius of starlikeness for harmonic mappings
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 16-24

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper we obtain the criterion of starlikeness of the image of the disk with center at the origin and radius $r\in(0,1)$ under univalent harmonic mapping by a function, which maps the unit disk onto a convex domain. This criterion is analogous to the criterion of image convexity, and it is expressed in terms of starlikeness in one direction. As a corollary we obtain new estimate for the radius of starlikeness of the class of univalent harmonic mappings which map the unit disk onto a convex domain. 
@article{ZNSL_2017_456_a1,
     author = {A. O. Bagapsh},
     title = {On the radius of starlikeness for harmonic mappings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {16--24},
     publisher = {mathdoc},
     volume = {456},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a1/}
}
TY  - JOUR
AU  - A. O. Bagapsh
TI  - On the radius of starlikeness for harmonic mappings
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 16
EP  - 24
VL  - 456
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a1/
LA  - ru
ID  - ZNSL_2017_456_a1
ER  - 
%0 Journal Article
%A A. O. Bagapsh
%T On the radius of starlikeness for harmonic mappings
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 16-24
%V 456
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a1/
%G ru
%F ZNSL_2017_456_a1
A. O. Bagapsh. On the radius of starlikeness for harmonic mappings. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 16-24. http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a1/