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Let $\mathcal{A}_n$ be the class of analytic functions $f(z)$ of the form $f(z)=z+\sum_{k=n+1}^\infty a_kz^k$, $n\in\mathbb{N}$ defined on the open unit disk $\mathbb{D}$, and let \begin{align*} \Omega_n:=\left\{f\in\mathcal{A}_n:\left|zf'(z)-f(z)\right|<\frac{1}{2},\; z\in\mathbb{D}\right\}. \end{align*} In this paper, we make use of differential subordination technique to obtain sufficient conditions for the class $\Omega_n$. Writing $\Omega:=\Omega_1$, we obtain inclusion properties of $\Omega$ with respect to functions which map $\mathbb{D}$ onto certain parabolic regions and as a consequence, establish a relation connecting the parabolic starlike class $\mathcal{S}_P$ and the uniformly starlike $UST$. Various radius problems for the class $\Omega$ are considered and the sharpness of the radii estimates is obtained analytically besides graphical illustrations.
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참고문헌 (23)
참고문헌 신청
R. M. Ali / 2011 / Uniformly convex and uniformly starlike functions / Math. Newsletter 21(1):16~30
R. Bharati / 1997 / On subclasses of uniformly convex functions and corresponding class of starlike functions / Tamkang J. Math 28(1):17~32
T. Bulboacˇa / 2005 / Differential Subordinations and Superordinations: Recent Results / House of Scientific Book Publ
N. E. Cho / 2019 / Radius Problems for Starlike Functions Associated with the Sine Function / Bulletin of the Iranian Mathematical Society 45(1):213~232
P. L. Duren / 1983 / Univalent Functions / Springer-Verlag
R. Bharati / 1997 / On subclasses of uniformly convex functions and corresponding class of starlike functions / Tamkang J. Math 28(1):17~32
T. Bulboacˇa / 2005 / Differential Subordinations and Superordinations: Recent Results / House of Scientific Book Publ
N. E. Cho / 2019 / Radius Problems for Starlike Functions Associated with the Sine Function / Bulletin of the Iranian Mathematical Society 45(1):213~232
P. L. Duren / 1983 / Univalent Functions / Springer-Verlag
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