Some extension results concerning analytic and meromorphic multivalent functions
Bull. Korean Math. Soc. 2019 Vol. 56, No. 4, 911-927
https://doi.org/10.4134/BKMS.b180679
Published online July 31, 2019
Ali Ebadian, Vali Soltani Masih, Shahram Najafzadeh
Urmia university; Payame Noor University(PNU); Payame Noor University(PNU)
Abstract : Let $\mathscr{B}_{p,n}^{\upeta, \upmu}\left(\upalpha\right)$; $\left( \upeta, \upmu\in \mathbb{R}, n,p\in \mathbb{N}\right) $ denote all functions $f$ class in the unit disk $\mathbb{U}$ as $f(z)=z^p+\sum_{k=n+p}^{\infty}a_kz^k$ which satisfy: \begin{align*} & \left| \left[ \frac{f'(z)}{pz^{p-1}}\right]^{\upeta} \left[ \frac{z^p}{f(z)}\right] ^{\upmu}-1\right| <1-\frac{\upalpha}{p}; \quad \left( z\in \mathbb{U}, \: 0\leq \upalpha
Keywords : multivalent functions, multivalent meromorphic functions, punctured unit disk, Jack's Lemma, $p$-valent strongly starlike and convex functions of order $\upgamma$ and type $\upbeta$
MSC numbers : Primary 30C45, 30A10
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