TY - JOUR
T1 - ON CONVEX COMBINATIONS of CONVEX HARMONIC MAPPINGS
AU - Ferrada-Salas, Álvaro
AU - Hernández, Rodrigo
AU - Martín, María J.
N1 - Funding Information:
The second and third authors are supported by Fondecyt, Chile, grant 1150284. The third author is also partially supported by grant MTM2015-65792-P from MINECO/FEDER, the Thematic Research Network MTM2015-69323-REDT, MINECO, Spain, and the Academy of Finland, grant 268009.
Publisher Copyright:
© 2017 Australian Mathematical Publishing Association Inc.
PY - 2017/10/1
Y1 - 2017/10/1
N2 - The family Fλ of orientation-preserving harmonic functions f = h+g in the unit disc (normalised in the standard way) satisfying {equation presented} for some {equation presented} , along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in Fλ are convex.
AB - The family Fλ of orientation-preserving harmonic functions f = h+g in the unit disc (normalised in the standard way) satisfying {equation presented} for some {equation presented} , along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in Fλ are convex.
KW - convex combinations
KW - convex harmonic mappings
UR - http://www.scopus.com/inward/record.url?scp=85026900736&partnerID=8YFLogxK
U2 - 10.1017/S0004972717000685
DO - 10.1017/S0004972717000685
M3 - Article
AN - SCOPUS:85026900736
VL - 96
SP - 256
EP - 262
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
SN - 0004-9727
IS - 2
ER -