Some properties related to a certain class of starlike functions

Raina, Ravinder Krishna; Sokół, Janusz

doi:10.1016/j.crma.2015.09.011

Complex analysis

Some properties related to a certain class of starlike functions
[Quelques propriétés liées à une classe de fonctions étoilées]

Présenté par : the Editorial Board

Raina, Ravinder Krishna ¹ ; Sokół, Janusz 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, Tome 353 (2015) no. 11, pp. 973-978.

Résumé
Abstract

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.

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)} |

| 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.

Reçu le : 2015-05-13
Accepté le : 2015-09-14
Publié le : 2015-10-19

DOI : 10.1016/j.crma.2015.09.011

Affiliations des auteurs :

Raina, Ravinder Krishna ¹ ; Sokół, Janusz 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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Raina, Ravinder Krishna; Sokół, Janusz. Some properties related to a certain class of starlike functions. Comptes Rendus. Mathématique, Tome 353 (2015) no. 11, pp. 973-978. doi : 10.1016/j.crma.2015.09.011. http://archive.numdam.org/articles/10.1016/j.crma.2015.09.011/

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