L. Trojnar-Spelina | Searcharxiv

arXiv2018

Some applications of differential subordination for certain starlike functions

We consider the class $\mathcal{S}^*(q_c)$ of normalized starlike functions $f$ analytic in the open unit disk $|z|<1$ that satisfying the inequality \begin{equation*} \left|\left(\frac{zf'(z)}{f(z)}\right)^2-1\right|<c \quad (0<c\leq1). \end{equation*} In this article, we present some subordination relations and these relations are then used to obtain some corollaries for some subclass of analytic functions.

math.CV↗

arXiv2018

Further results for starlike functions related with Booth lemniscate

In this paper we investigate an interesting subclass $\mathcal{BS}(α)$ ($0\leq α<1$) of starlike functions in the unit disk $Δ$. The class $\mathcal{BS}(α)$ was introduced by Kargar et al. [R. Kargar, A. Ebadian and J. Sokół, {\it On Booth lemniscate and starlike functions}, Anal. Math. Phys. (2017) DOI: 10.1007/s13324-017-0187-3] which is strongly related to the Booth lemniscate. Some geometric properties of this class of analytic functions including, radius of starlikeness of order $γ$ ($0\leqγ<1$), the image of $f(\{z:|z|<r\})$ when $f\in \mathcal{BS}(α)$, an special example and estimate of bounds for ${\rm Re}\{f(z)/z\}$ are studied.

math.CV↗