On coefficients of some p-valent starlike functions

Mamoru Nunokawa, Janusz Sokol, Nikola Tuneski


We consider the class $\mathcal A_p$ of functions $f$ analytic in
the unit disk $|z|<1$ in the complex plane, of the form
$f(z)=z^p+\ldots$ such that $\mathfrak{Re}
zf^{(p)}(z)/f^{(p-1)}(z)>0$ in the unit disc. The object  of the
present paper is to derive some bounds for coefficients in this
class and relation with the functions satisfying  condition
$\mathfrak{Re} f^{(k)}(z)/f^{(p-k)}(z)>0$ in the unit disc.


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