Linear combinations of harmonic quasiconformal mappings convex in one direction

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 -