Coefficient Estimates and Other Properties for a Class of Spirallike Functions Associated with a Differential Operator

Abstract

For , , , $0\le \beta \le \alpha$, and $m\in \mathbb{N}\cup \{0\}$, a new class $S_{\alpha ,\beta }^m(\eta ,\gamma ,\lambda )$ of analytic functions defined by means of the differential operator $D_{\alpha ,\beta }^m$ is introduced. Our main object is to provide sharp upper bounds for Fekete-Szegö problem in $S_{\alpha ,\beta }^m(\eta ,\gamma ,\lambda )$. We also find sufficient conditions for a function to be in this class. Some interesting consequences of our results are pointed out.