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For given non-negative real numbers $\alpha_k$ with $ \sum_{k=1}^{m}\alpha_k =1$ and normalized analytic functions $f_k$, $k=1,\dotsc,m$, defined on the open unit disc, let the functions $F$ and $F_n$ be defined by $ F(z):=\sum_{k=1}^{m}\alpha_k f_k
Externí odkaz:
http://arxiv.org/abs/2201.01475
Autor:
Malik, Somya, Ravichandran, V.
For a function $f$ starlike of order $\alpha$, $0\leqslant \alpha <1$, a non-constant polynomial $Q$ of degree $n$ which is non-vanishing in the unit disc $\mathbb{D}$ and $\beta>0$, we consider the function $F:\mathbb{D}\to\mathbb{C}$ defined by $F(
Externí odkaz:
http://arxiv.org/abs/2201.01473
The function $G_\alpha(z)=1+ z/(1-\alpha z^2)$, \, $0\leq \alpha <1$, maps the open unit disc $\mathbb{D}$ onto the interior of a domain known as the Booth lemniscate. Associated with this function $G_\alpha$ is the recently introduced class $\mathca
Externí odkaz:
http://arxiv.org/abs/2201.01042
Autor:
Malik, Somya, Ravichandran, V.
For normalised analytic functions $f$ defined on the open unit disc $\mathbb{D}$ satisfying the condition $\sup_{z\in \mathbb{D}}(1-|z^2|) |f'(z)|\leq 1$, known as Bloch functions, we determine various starlikeness radii.
Externí odkaz:
http://arxiv.org/abs/2011.09234
Akademický článek
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Autor:
Malik, Somya, Ravichandran, V.
Publikováno v:
The Journal of Analysis; March 2023, Vol. 31 Issue: 1 p201-228, 28p
