Univalency of certain analytic functions

Abstract

Let $\mathcal{A}$ be the class of functions $f(z)$ which are analytic in the open unit disk $\mathbf{U}$ with $f(0) = 0$ and $f'(0) = 1$. Using $g(z) \in \mathcal{A}$, the subclass $\mathcal{T}(\lambda, \mu, g)$ of $\mathcal{A}$ consisting of functions $f(z)$ is introduced. The object of the present paper is to consider some univalence conditions for functions $f(z)$ belonging to the class $\mathcal{T}(\lambda, \mu, g)$ applying the subordination properties of analytic functions.