Support points of some classes of analytic and univalent functions

Vasudevarao Allu; Abhishek Pandey

doi:10.5802/crmath.181

Analyse et géométrie complexes

Support points of some classes of analytic and univalent functions

Vasudevarao Allu ¹ ; Abhishek Pandey ¹

¹ School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Argul, Bhubaneswar, PIN-752050, Odisha (State), India

Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 465-473.

Résumé

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

|f^{'} (z) {(\frac{z}{f (z)})}^{2} - 1| < 1 for z \in 𝔻,

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

ℜ (1 + \frac{z f^{''} (z)}{f^{'} (z)}) > - \frac{1}{2} for z \in 𝔻 .

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

Reçu le : 2020-11-02
Accepté le : 2021-01-19
Publié le : 2021-06-17

Zbl

DOI : 10.5802/crmath.181

Classification : 30C45, 30C50

Affiliations des auteurs :

Vasudevarao Allu ¹ ; Abhishek Pandey ¹

¹ School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Argul, Bhubaneswar, PIN-752050, Odisha (State), India

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Support points of some classes of analytic and univalent functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {465--473},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
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     year = {2021},
     doi = {10.5802/crmath.181},
     zbl = {07362166},
     language = {en},
}

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Vasudevarao Allu; Abhishek Pandey. Support points of some classes of analytic and univalent functions. Comptes Rendus. Mathématique, Volume 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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