Add to ORKGLet $\mathcal{S}$ denote the class of analytic and univalent ({\it i.e.}, one-to-one) functions $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$. For $f\in \mathcal{S}$, Ma proposed the generalized Zalcman conjecture that $$|a_{n}a_{m}-a_{n+m-1}|\le (n-1)(m-1),\,\,\,\mbox{ for } n\ge2,\, m\ge 2,$$ with equality only for the Koebe function $k(z) = z/(1 - z)^2$ and its rotations. In this paper using the properties of holomorphic motion and Krushkal's Surgery Lemma \cite{Krushkal-1995}, we prove the generalized Zalcman conjecture when $n=2$, $m=3$ and $n=2$, $m=4$.Comment: 14 pages. arXiv admin note: text overlap with arXiv:2209.1059
summary:Let $S$ denote the class of functions $f(x)=z+a_2z^2+a_3z^3+\ldots$ univalent and holomorphi...
Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departament...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46267/1/209_2005_Article_BF01214860.pd
Let $\mathcal{S}$ denote the class of analytic and univalent ({\it i.e.}, one-to-one) functions $ f(...
AbstractZalcman conjectured that |a2n−a2n−1|≤(n−1)2,n=2,3,… forf(z)=z+a2z2+a3z3+···∈S, the class of ...
AbstractZalcman conjectured that |a2n−a2n−1|≤(n−1)2,n=2,3,… forf(z)=z+a2z2+a3z3+···∈S, the class of ...
This is the peer-reviewed version of the following article: Efraimidis, I., & Vukotić, D. Applicatio...
This is the peer-reviewed version of the following article: Efraimidis, I., & Vukotić, D. Applicatio...
Let $\mathcal{A}$ denote the class of analytic functions in the unit disk $\mathbb{D}:=\{z\in\mathbb...
AbstractIn this article, by employing the hyperbolic tangent function tanhz, a subfamily$\mathcal{S}...
The aim of this paper is to give some applications of Zalcman's Rescalling Lemma.Comment: 6 pages, w...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135462/1/blms0193.pd
summary:Let $S$ denote the class of functions $f(z) = z + a_2z^2 + a_3z^3 + \ldots$ univalent and ho...
summary:Let $S$ denote the class of functions $f(z) = z + a_2z^2 + a_3z^3 + \ldots$ univalent and ho...
summary:Let $S$ denote the class of functions $f(x)=z+a_2z^2+a_3z^3+\ldots$ univalent and holomorphi...
summary:Let $S$ denote the class of functions $f(x)=z+a_2z^2+a_3z^3+\ldots$ univalent and holomorphi...
Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departament...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46267/1/209_2005_Article_BF01214860.pd
Let $\mathcal{S}$ denote the class of analytic and univalent ({\it i.e.}, one-to-one) functions $ f(...
AbstractZalcman conjectured that |a2n−a2n−1|≤(n−1)2,n=2,3,… forf(z)=z+a2z2+a3z3+···∈S, the class of ...
AbstractZalcman conjectured that |a2n−a2n−1|≤(n−1)2,n=2,3,… forf(z)=z+a2z2+a3z3+···∈S, the class of ...
This is the peer-reviewed version of the following article: Efraimidis, I., & Vukotić, D. Applicatio...
This is the peer-reviewed version of the following article: Efraimidis, I., & Vukotić, D. Applicatio...
Let $\mathcal{A}$ denote the class of analytic functions in the unit disk $\mathbb{D}:=\{z\in\mathbb...
AbstractIn this article, by employing the hyperbolic tangent function tanhz, a subfamily$\mathcal{S}...
The aim of this paper is to give some applications of Zalcman's Rescalling Lemma.Comment: 6 pages, w...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135462/1/blms0193.pd
summary:Let $S$ denote the class of functions $f(z) = z + a_2z^2 + a_3z^3 + \ldots$ univalent and ho...
summary:Let $S$ denote the class of functions $f(z) = z + a_2z^2 + a_3z^3 + \ldots$ univalent and ho...
summary:Let $S$ denote the class of functions $f(x)=z+a_2z^2+a_3z^3+\ldots$ univalent and holomorphi...
summary:Let $S$ denote the class of functions $f(x)=z+a_2z^2+a_3z^3+\ldots$ univalent and holomorphi...
Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departament...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46267/1/209_2005_Article_BF01214860.pd