Turkish Journal of Mathematics
Article Title
Some properties for a class of analytic functions defined by a higher-order differential inequality
DOI
10.3906/mat-1906-65
Abstract
Let $\mathcal{B}_p(\alpha,\beta, \lambda;j)$ be the class consisting of functions $f(z)= z^p+\sum_{k=p+1}^{\infty}a_k z^{k},\; p\in \mathbb{N}$ which satisfy $ \mathrm{Re}\left\{\alpha\frac{f^{(j)}(z)}{z^{p-j}}+\beta\frac{f^{(j+1)}(z)}{z^{p-j-1}}+\left(\frac{\beta-\alpha}{2}\right)\frac{f^{(j+2)}(z)}{z^{p-j-2}}\right\}>\lambda,\;\;(z\in \mathbb{U}=\{z:\; z (5-12\ln 2)/(44-48\ln 2)\approx -0.309$ is sufficient condition for any normalized analytic function $f$ to be starlike in $\mathbb{U}$. The results improve and include a number of known results as their special cases.
First Page
2473
Last Page
2493
Recommended Citation
ALREFAI, OQLAH
(2019)
"Some properties for a class of analytic functions defined by a higher-order differential inequality,"
Turkish Journal of Mathematics: Vol. 43:
No.
5, Article 33.
https://doi.org/10.3906/mat-1906-65
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss5/33
