Some properties related to a certain class of starlike functions

Ravinder Krishna Raina; Janusz Sokół

doi:10.1016/j.crma.2015.09.011

Complex analysis

Some properties related to a certain class of starlike functions

Presented by: the Editorial Board

Ravinder Krishna Raina ¹; Janusz Sokół ²

¹ M.P. University of Agriculture and Technology, Udaipur, India
² Department of Mathematics, Rzeszów University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland

Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 973-978.

Abstract
Résumé

This paper considers a class $Δ^{⁎}$ of normalized starlike functions f analytic in the open unit disk $| z | < 1$ satisfying the inequality that

| {\frac{z f^{'} (z)}{f (z)}}^{2} - 1 | < 2 | \frac{z f^{'} (z)}{f (z)} |

in

| z | < 1

. We first show that the class

S^{⁎} (q)

(defined below) is a subclass of

Δ^{⁎}

and then obtain some useful properties of these classes of functions.

Nous considérons dans cette Note une classe $Δ^{⁎}$ de fonctions étoilées normalisées f, analytiques dans le disque unité ouvert $| z | < 1$ et y satisfaisant l'inégalité

| {\frac{z f^{'} (z)}{f (z)}}^{2} - 1 | < 2 | \frac{z f^{'} (z)}{f (z)} | .

Nous montrons d'abord que la classe

S^{⁎} (q)

(définie ci-dessous) est une sous-classe de

Δ^{⁎}

, puis nous obtenons quelques propriétés utiles de ces classes de fonctions.

Received: 2015-05-13
Accepted: 2015-09-14
Published online: 2015-10-19

DOI: 10.1016/j.crma.2015.09.011

Author's affiliations:

Ravinder Krishna Raina ¹; Janusz Sokół ²

¹ M.P. University of Agriculture and Technology, Udaipur, India
² Department of Mathematics, Rzeszów University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland

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     title = {Some properties related to a certain class of starlike functions},
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     number = {11},
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     language = {en},
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Ravinder Krishna Raina; Janusz Sokół. Some properties related to a certain class of starlike functions. Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 973-978. doi : 10.1016/j.crma.2015.09.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.09.011/

References
Cited by

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[11] R.K. Raina, J. Sokół, On some class of starlike functions, Filomat, submitted for publication.

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