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# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## Coefficient inequalities for concave and meromorphically starlike univalent functions

### Tom 93 / 2008

Annales Polonici Mathematici 93 (2008), 177-186 MSC: Primary 30C45. DOI: 10.4064/ap93-2-6

#### Streszczenie

Let $\mathbb D$ denote the open unit disk and $f:\mathbb D\rightarrow\overline{\mathbb C}$ be meromorphic and univalent in $\mathbb D$ with a simple pole at $p\in (0,1)$ and satisfying the standard normalization $f(0)=f'(0)-1=0$. Also, assume that $f$ has the expansion $$f(z)=\sum_{n=-1}^{\infty}a_n(z-p)^n,\quad |z-p|<1-p,$$ and maps $\mathbb D$ onto a domain whose complement with respect to $\overline{\mathbb C}$ is a convex set (starlike set with respect to a point $w_0\in \mathbb C, w_0\neq 0$ resp.). We call such functions concave (meromorphically starlike resp.) univalent functions and denote this class by ${\rm Co}(p)$ $({\mit\Sigma}^{\rm s}(p, w_0)$ resp.). We prove some coefficient estimates for functions in these classes; the sharpness of these estimates is also established.

#### Autorzy

• B. BhowmikDepartment of Mathematics
Chennai 600 036, India
e-mail
• S. PonnusamyDepartment of Mathematics