Weighted composition operators on the class of subordinate functions

Abstract: 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 $|\alpha|\leq 1, \alpha \neq -1$. Some of its consequences and examples for some special cases are presented. Furthermore, we discuss about the fixed points of weighted composition operators.