The Norm Estimates of Pre-Schwarzian Derivatives of Spirallike Functions and Uniformly Convex $alpha$-spirallike Functions
| Autor: | Zahra Orouji, Rasul Aghalary |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Sahand Communications in Mathematical Analysis, Vol 12, Iss 1, Pp 89-96 (2018) |
| Druh dokumentu: | article |
| ISSN: | 2322-5807 2423-3900 |
| DOI: | 10.22130/scma.2018.68371.262 |
| Popis: | For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$, we definea subclass of the spirallike functions, $SP_{p}(alpha)$, the setof all functions $fin mathcal{A}$[releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.]In the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative $mathrm{T}_f=f''/f'$ where $|mathrm{T}_f|=sup_{zin Delta} (1-|z|^2)|mathrm{T}_f(z)|$ for the functions in $SP_{p}(alpha)$. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|