Coefficient estimates of negative powers and inverse coefficients for certain starlike functions
Click here to view fulltext PDF
Permanent link:
http://www.ias.ac.in/article/fulltext/pmsc/127/03/0449-0462
Univalent; starlike; meromorphic functions; subordination; coefficient bounds; inverse coefficient bounds
For −1 $\leq B < A \leq 1$, let $S^{\ast}(A,B)$ denote the class of normalized analytic functions $f(z) = z+\sum^{\infty}_{n=2}a_{n}z^{n}$ in $\mid z\mid <1$ which satisfy the subordination relation $zf'(z)/f(z)\prec(1+Az)/(1+Bz)$ and $\sum^{\ast}(A,B)$ be the corresponding class of meromorphic functions in $\mid z\mid > 1$. For $f \in S^{\ast}(A,B)$ and $\lambda > 0$, we shall estimate the absolute value of the Taylor coefficients $a_{n}(−\lambda,f )$ of the analytic function $(f(z)/z)^{−\lambda}$. Using this we shall determine the coefficient estimate for inverses of functions in the classes $S^{\ast}(A,B)$ and $\sum^{\ast}(A,B)$.
MD FIROZ ALI^{1} ^{} A VASUDEVARAO^{1} ^{}
Current Issue
Volume 127 | Issue 5
November 2017
© 2017 Indian Academy of Sciences, Bengaluru.