TY - JOUR
ID - 696730
TI - On Some Properties of Log-Harmonic Functions Product
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Alizadeh, Mehri
AU - Aghalary, Rasoul
AU - Ebadian, Ali
AD - Department of Mathematics, Faculty of Science, PNU University, P.O.BOX 19395-4697, Tehran, Iran.
AD - Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.
Y1 - 2022
PY - 2022
VL - 19
IS - 4
SP - 133
EP - 147
KW - Univalent function
KW - Log-harmonic function
KW - Convex in the one direction
KW - Sense-preserving functions
DO - 10.22130/scma.2022.554936.1121
N2 - In this paper we define a new subclass $S_{LH}(k, \gamma; \varphi)$ of log-harmonic mappings, and then basic properties such as dilations, convexity on one direction and convexity of log functions of convex- exponent product of elements of that class are discussed. Also we find sufficient conditions on $\beta$ such that $f\in S_{LH}(k, \gamma; \varphi)$ leads to $F(z)=f(z)|f(z)|^{2\beta}\in S_{LH}(k, \gamma, \varphi)$. Our results generalize the analogues of the earlier works in the combinations of harmonic functions.
UR - https://scma.maragheh.ac.ir/article_696730.html
L1 - https://scma.maragheh.ac.ir/article_696730_4a7b7f85d03691ff0c0c19b7873399e4.pdf
ER -