A new subclass of analytic functions and some results related to Booth lemniscate

Abstract

In this paper, we introduce the subclass $\mathcal{K}\mathcal{S}(\alpha)$ of univalent functions in $\mathcal{A}$ and study some properties of this class. We apply matters of differential subordinations, to investigate some results concerning the subclasses $\mathcal{K}\mathcal{S}(\alpha)$ and $\mathcal{B}\mathcal{S}(\alpha)$ of $\mathcal{A}$, where $\alpha \in [0,1)$.