%0 Journal Article
%T On Some Properties of Log-Harmonic Functions Product
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Alizadeh, Mehri
%A Aghalary, Rasoul
%A Ebadian, Ali
%D 2022
%\ 10/01/2022
%V 19
%N 4
%P 133-147
%! On Some Properties of Log-Harmonic Functions Product
%K Univalent function
%K Log-harmonic function
%K Convex in the one direction
%K Sense-preserving functions
%R 10.22130/scma.2022.554936.1121
%X 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.
%U https://scma.maragheh.ac.ir/article_696730_4a7b7f85d03691ff0c0c19b7873399e4.pdf