Complex analysis
Some properties related to a certain class of starlike functions
Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 973-978.

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

|{zf(z)f(z)}21|<2|zf(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

|{zf(z)f(z)}21|<2|zf(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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.09.011
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, Volume 353 (2015) no. 11, pp. 973-978. doi : 10.1016/j.crma.2015.09.011. http://www.numdam.org/articles/10.1016/j.crma.2015.09.011/

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