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- W2979673732 abstract "A function $fin mathcal{A}_1$ is said to be stable with respect to $gin mathcal{A}_1 $ if begin{align*} frac{s_n(f(z))}{f(z)} prec frac{1}{g(z)}, qquad zinmathbb{D}, end{align*} holds for all $n in mathbb{N}$ where $mathcal{A}_1$ denote the class of analytic functions $f$ in the unit disk $mathbb{D} ={zin mathbb{C}: |z|<1 }$ normalized by $f(0)=1$. Here $s_n(f(z))$, the $n^{th}$ partial sum of $f(z)=displaystylesum_{k=0}^{infty} a_kz^k$ is given by $s_n(f(z)) = displaystylesum_{k=0}^{n} a_kz^k, nin mathbb{N} cup {0}$. In this work, we consider the following function begin{align*} v_{lambda}(A,B,z)=left(frac{1+Az}{1+Bz}right)^{lambda} end{align*} for $-1leq B < A leq 1$ and $0leq lambda leq 1 $ for our investigation. The main purpose of this paper is to prove that $v_{lambda}(A,B,z)$ is stable with respect to $displaystyle v_{lambda}(0,B,z)= frac{1}{(1+Bz)^{lambda}}$ for $0 < lambda leq 1 $ and $-1leq B < A leq 0$. Further, we prove that $v_{lambda}(A,B,z)$ is not stable with respect to itself, when $0 < lambda leq 1 $ and $-1leq B < A <0$. end{abstract}" @default.
- W2979673732 created "2019-10-18" @default.
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- W2979673732 date "2019-10-14" @default.
- W2979673732 modified "2023-09-26" @default.
- W2979673732 title "Stable Functions of Janowski Type" @default.
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