Weighted composition operators on the class of subordinate functions

In this article, we study the weighted composition operators preserving the class ${\mathcal{P}}_{\alpha }$ of analytic functions subordinate to $\frac{1+\alpha z}{1-z}$ for $\mathrm{\mid }\alpha \mathrm{\mid }\le 1,\alpha \mathrm{\ne }-1$. Some of its consequences and examples for some special cases are presented. Furthermore, we discuss about the fixed points of weighted composition operators.