TY - JOUR
T1 - Convolutions of Harmonic Right Half-Plane Mappings with Harmonic Strip Mappings
AU - Liu, Zhi Hong
AU - Wang, Zhi Gang
AU - Rasila, Antti
AU - Jiang, Yue Ping
N1 - Publisher Copyright:
© 2019, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.
PY - 2019/5/15
Y1 - 2019/5/15
N2 - We prove that convolutions of harmonic right half-plane mappings with harmonic vertical strip mappings are univalent and convex in the horizontal direction. The proofs of these results make use the Gauss–Lucas Theorem. Our results show that two recent conjectures, the one by Kumar, Gupta, Singh and Dorff, and the one of Liu, Jiang and Li, are true. Moreover, examples of univalent harmonic mappings related to the above-mentioned results are presented, suggesting that the bounds given by our results may be sharp.
AB - We prove that convolutions of harmonic right half-plane mappings with harmonic vertical strip mappings are univalent and convex in the horizontal direction. The proofs of these results make use the Gauss–Lucas Theorem. Our results show that two recent conjectures, the one by Kumar, Gupta, Singh and Dorff, and the one of Liu, Jiang and Li, are true. Moreover, examples of univalent harmonic mappings related to the above-mentioned results are presented, suggesting that the bounds given by our results may be sharp.
KW - Gauss–Lucas Theorem
KW - Harmonic convolution
KW - Harmonic half-plane mappings
KW - Harmonic vertical strip mappings
UR - http://www.scopus.com/inward/record.url?scp=85071677448&partnerID=8YFLogxK
U2 - 10.1007/s40840-019-00720-0
DO - 10.1007/s40840-019-00720-0
M3 - 文章
AN - SCOPUS:85071677448
SN - 0126-6705
VL - 42
SP - 1199
EP - 1212
JO - Bulletin of the Malaysian Mathematical Sciences Society
JF - Bulletin of the Malaysian Mathematical Sciences Society
IS - 3
ER -