Coefficient Estimates for Sakaguchi Type Functions

Abstract

Let $S_{\lambda ,\mu }^{n}(\alpha ,t)$ be the class of normalized analytic functions defined in the open unit disk satisfying
\begin{equation*}
\Re \left( \frac{(1-t)z\left( D_{\lambda ,\mu }^{n}f(z)\right)
^{\prime }}{ D_{\lambda ,\mu }^{n}f(z)-D_{\lambda ,\mu
}^{n}f(tz)}\right) >\alpha \text{, \ \ }\left\vert t\right\vert
\leq 1,\text{ }t\neq 1
\end{equation*}
for some $\alpha (0\leq \alpha <1)$ and $D_{\lambda ,\mu }^{n}$ is a linear multiplier differential operator defined by the authors in \cite{DeOr}. The object of the present paper is to discuss some properties of functions $f(z)$ belonging to the classes $S_{\lambda ,\mu }^{n}(\alpha ,t)$ and $T_{\lambda ,\mu }^{n}(\alpha ,t)$ where $f(z)\in T_{\lambda ,\mu }^{n}(\alpha ,t)$ if and only if $zf^{\prime }(z)\in S_{\lambda ,\mu }^{n}(\alpha ,t).$

2000 Mathematics Subject Classification. 30C45