TY - JOUR
T1 - Linear combinations of harmonic quasiconformal mappings convex in one direction
AU - Sun, Yong
AU - Rasila, Antti
AU - Jiang, Yue Ping
N1 - Publisher Copyright:
© 2016, Tokyo Institute of Technology. All rights reserved.
PY - 2016
Y1 - 2016
N2 - In this paper, we introduce a new class (Formula presented) (k; γ; ɸ) of harmonic quasiconformal mappings, where k ∈ [0, 1), γ ∈ [0, π) and ɸ is an analytic function. Sufcient conditions for the linear combinations of mappings in such classes to be in a similar class, and convex in a given direction, are established. In particular, we prove that the images of linear combinations in this class, for special choices of γ and ɸ, are convex.
AB - In this paper, we introduce a new class (Formula presented) (k; γ; ɸ) of harmonic quasiconformal mappings, where k ∈ [0, 1), γ ∈ [0, π) and ɸ is an analytic function. Sufcient conditions for the linear combinations of mappings in such classes to be in a similar class, and convex in a given direction, are established. In particular, we prove that the images of linear combinations in this class, for special choices of γ and ɸ, are convex.
KW - Convex in one direction
KW - Harmonic K-quasiconformal mapping
KW - Linear combination
KW - Univalent harmonic mapping
UR - http://www.scopus.com/inward/record.url?scp=84978252290&partnerID=8YFLogxK
U2 - 10.2996/kmj/1467830143
DO - 10.2996/kmj/1467830143
M3 - 文章
AN - SCOPUS:84978252290
SN - 0386-5991
VL - 39
SP - 366
EP - 377
JO - Kodai Mathematical Journal
JF - Kodai Mathematical Journal
IS - 2
ER -