Inequalities for fixed points of the subclass P(j,λ,α,n) of starlike functions with negative coefficients

Abstract

We consider the subclass $% P(j,\lambda ,\alpha ,n)$ of starlike functions with negative coefficients by using the differential $D^{n}$ operator and functions of the form $% f(z)=z-\sum\limits_{k=j+1}^{\infty }a_{k}z^{k}$ which are analytic in the open unit disk. We examine the subclass $P(j,\lambda ,\alpha ,n$,$z_{0})$ for which $f(z_{0})=z_{0}$ or $f^{^{\prime }}(z_{0})=1$, $z_{0}$ real. We determine coefficient inequalities for functions belonging to the class $% P(j,\lambda ,\alpha ,n$,$z_{0}).$ As special cases, the results of our paper reduce to Silverman [1].