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Comptes Rendus Mathématique
Volume 352, n° 11
pages 895-900 (novembre 2014)
Doi : 10.1016/j.crma.2014.09.015
Received : 30 April 2014 ;  accepted : 18 September 2014
On the class of bi-univalent functions
Sur la classe des fonctions bi-univalentes
 

Srikandan Sivasubramanian a, 1 , Radhakrishnan Sivakumar a , Teodor Bulboacă b, 2 , Tirunelveli Nellaiappar Shanmugam c
a Department of Mathematics, University College of Engineering Tindivanam, Anna University, Chennai, Tindivanam, 604 001, India 
b Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania 
c Department of Mathematics, University College of Engineering, Kanchipuram, Anna University, Chennai, Kanchipuram, 631 552, India 

Abstract

In an attempt to answer the question raised by A.W. Goodman, we obtain a covering theorem, a distortion theorem, a growth theorem, the radius of convexity and an argument estimate of   for functions of the class σ of bi-univalent functions.

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Résumé

Dans une tentative de répondre à une question posée par A.W. Goodman, nous obtenons des théorèmes de surjectivité, de déformation et de croissance, ainsi qu'une estimation du rayon de convexité et de l'argument de   pour une fonction f dans la classe σ des fonctions bi-univalentes .

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