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Comptes Rendus Mathématique
Volume 353, n° 7
pages 617-622 (juillet 2015)
Doi : 10.1016/j.crma.2015.03.016
Received : 14 January 2015 ;  accepted : 30 Mars 2015
The Fekete–Szegö functional associated with k -th root transformation using quasi-subordination
La fonctionnelle de Fekete–Szegö associée aux transformations racine   utilisant la subordination
 

Palpandy Gurusamy a , Janusz Sokół b , Srikandan Sivasubramanian c
a Department of Mathematics, Velammal Engineering College, Surapet, Chennai, 600 066, India 
b Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland 
c Department of Mathematics, University College of Engineering, Anna University, Tindivanam, 604 001, India 

Abstract

Quasi-subordination is an underlying concept in the area of complex function theory. It is an interesting topic that unifies the concept of both subordination and majorization. There has been no work in this area for the past three decades except possibly a recent article (Haji Mohd and Darus, Fekete–Szegö problems for quasi-subordination classes, Abstr. Appl. Anal. 2012 (2012) 192956, 14 p.) [[8]]. Exploiting this article, we provide an estimate with k -th root transform for certain classes of analytic univalent functions using quasi-subordination. The authors sincerely hope that this article will revive this concept and encourage other researchers to work in this quasi-subordination in the near-future in the area of complex function theory.

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Résumé

La quasi-subordination est un concept sous-jacent de la théorie des fonctions complexes. C'est un sujet intéressant, qui unifie les concepts de subordination et de majoration. Il n'y a pas eu de travaux dans ce domaine au cours des trois dernières décennies, à part, peut-être, un article récent (Haji Mohd and Darus, Fekete–Szegö problems for quasi-subordination classes, Abstr. Appl. Anal. 2012 (2012) 192956, 14 p.) [[8]]. Exploitant cet article, nous donnons une estimation avec les transformations racine   pour certaines classes de fonctions analytiques univalentes, utilisant la quasi-subordination. Les auteurs forment le vœu que cet article ravive l'intérêt pour ce concept et encourage, dans un proche avenir, d'autres chercheurs à le considérer en théorie des fonctions complexes.

The full text of this article is available in PDF format.


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