University of MaraghehSahand Communications in Mathematical Analysis2322-580719420221001On Some Properties of Log-Harmonic Functions Product13314769673010.22130/scma.2022.554936.1121ENMehriAlizadehDepartment of Mathematics, Faculty of Science, PNU University, P.O.BOX 19395-4697, Tehran, Iran.RasoulAghalaryDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.AliEbadianDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.Journal Article20220531In 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.https://scma.maragheh.ac.ir/article_696730_4a7b7f85d03691ff0c0c19b7873399e4.pdf