• P Vasundhra

Articles written in Proceedings – Mathematical Sciences

• Univalence and Starlikeness of Nonlinear Integral Transform of Certain Class of Analytic Functions

Let $\mathcal{U}(\lambda, \mu)$ denote the class of all normalized analytic functions 𝑓 in the unit disk $|z| &lt; 1$ satisfying the condition

For $f\in\mathcal{U}(\lambda, \mu)$ with $\mu\leq 1$ and $0\neq\mu_1\leq 1$, and for a positive real-valued integrable function 𝜑 defined on [0,1] satisfying the normalized condition $\int^1_0\varphi(t)dt=1$, we consider the transform $G_\varphi f(z)$ defined by

In this paper, we find conditions on the range of parameters 𝜆 and 𝜇 so that the transform $G_\varphi f$ is univalent or star-like. In addition, for a given univalent function of certain form, we provide a method of obtaining functions in the class $\mathcal{U}(\lambda, \mu)$.

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019