Analyse et géométrie complexes
Support points of some classes of analytic and univalent functions
Comptes Rendus. Mathématique, Tome 359 (2021) no. 4, pp. 465-473.

Let $𝒜$ denote the class of analytic functions in the unit disk $𝔻:=\left\{z\in ℂ:|z|<1\right\}$ satisfying $f\left(0\right)=0$ and ${f}^{\prime }\left(0\right)=1$. Let $𝒰$ be the class of functions $f\in 𝒜$ satisfying

 $\left|{f}^{\prime }\left(z\right){\left(\frac{z}{f\left(z\right)}\right)}^{2}-1\right|<1\phantom{\rule{1em}{0ex}}\phantom{\rule{4pt}{0ex}}\text{for}\phantom{\rule{4pt}{0ex}}z\in 𝔻,$

and $𝒢$ denote the class of functions $f\in 𝒜$ satisfying

 $\Re \left(1+\frac{z{f}^{\prime \prime }\left(z\right)}{{f}^{\prime }\left(z\right)}\right)>-\frac{1}{2}\phantom{\rule{1em}{0ex}}\phantom{\rule{4pt}{0ex}}\text{for}\phantom{\rule{4pt}{0ex}}z\in 𝔻.$

In the present paper, we characterize the set of support points of the classes $𝒰$ and $𝒢$.

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DOI : https://doi.org/10.5802/crmath.181
Classification : 30C45,  30C50
Vasudevarao Allu 1 ; Abhishek Pandey 1

1. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Argul, Bhubaneswar, PIN-752050, Odisha (State), India
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Vasudevarao Allu; Abhishek Pandey. Support points of some classes of analytic and univalent functions. Comptes Rendus. Mathématique, Tome 359 (2021) no. 4, pp. 465-473. doi : 10.5802/crmath.181. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.181/

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