Turkish Journal of Mathematics
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.
Keywords
Starlike functions, p-valent functions, Jack's lemma, univalent functions, extreme points, convex functions, distortion and growth theorem, coefficient bounds, differential inequality
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
