### On coefficients of some p-valent starlike functions

#### Abstract

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.

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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