On Certain Subclass of Analytic Functions with Fixed Point

Abstract

A new certain differential operator $T_{\alpha ,\beta ,\delta ,\lambda }^{m}f(z)$ and a subclass $S_{m,w}^{*}(\alpha ,\beta ,\gamma ,\delta ,\lambda )$ are introduced for functions of the form $f(z)=(z-w)-{\sum }_{n=2}^{\infty }{a}_n{(z-w)}^n$ which are univalent in the unit disc . In this paper, we obtain coefficient inequalities, distortion theorem, closure theorems, and class preserving integral operators of functions belonging to the class $S_{m,w}^{*}(\alpha ,\beta ,\gamma ,\delta ,\lambda )$.