On Some Applications of Noshiro-Warschawski's Theorem

Janusz Sok\'{o}\l, Mamoru Nunokawa, Nak Eun Cho, Huo Tang


We  apply  Noshiro-Warschawski's theorem to prove that if
$f(z)=z+a_2z^2+\cdots$ is analytic in $|z|<1$ and if $
\left|\mathfrak{Re}\{zf''(z)\}\right|\leq\alpha|z|^{\alpha}$ in
$|z|<1$, for some $\alpha>0$, then $f(z)$ is univalent in $|z|<1$.
Also, applying Ozaki's condition, we obtain several sufficient
conditions for functions to be $p$-valent or $p$-valently starlike
function in $|z|<1$.

Full Text:



  • There are currently no refbacks.