Bulletin of the
Korean Mathematical Society BKMS

For a given $p$-valent analytic function $g$ with positive
coefficients in the open unit disk $\UD$, we study a class of
functions $f(z)=z^p-\sum_{n=m}^\infty a_nz^n$\ ($a_n\geq 0$) satisfying
\[ \frac{1}{p}\Re \left( \frac{z(f*g)'(z)}{(f*g)(z)}\right)
> \alpha\quad (0\leq \alpha<1; z\in\Delta).\]
Coefficient inequalities, distortion and covering theorems, as
well as closure theorems are determined. The results obtained
extend several known results as special cases.

Keywords: starlike function, convolution, subordination, negative coefficients

MSC numbers: 30C45