Comptes Rendus
no. 7
Complex analysis
The Fekete–Szegö functional associated with k-th root transformation using quasi-subordination
[La fonctionnelle de Fekete–Szegö associée aux transformations racine ke utilisant la subordination]

Présenté par : the Editorial Board

Palpandy Gurusamy1 ; Janusz Sokół2 ; Srikandan Sivasubramanian3
1 Department of Mathematics, Velammal Engineering College, Surapet, Chennai, 600 066, India
2 Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
3 Department of Mathematics, University College of Engineering, Anna University, Tindivanam, 604 001, India
Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 617-622.

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 ke 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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.03.016
Palpandy Gurusamy 1 ; Janusz Sokół 2 ; Srikandan Sivasubramanian 3

1 Department of Mathematics, Velammal Engineering College, Surapet, Chennai, 600 066, India
2 Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
3 Department of Mathematics, University College of Engineering, Anna University, Tindivanam, 604 001, India 
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Palpandy Gurusamy; Janusz Sokół; Srikandan Sivasubramanian. The Fekete–Szegö functional associated with k-th root transformation using quasi-subordination. Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 617-622. doi : 10.1016/j.crma.2015.03.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.03.016/

[1] H.R. Abdel-Gawad On the Fekete–Szegö problem for alpha-quasi-convex functions, Tamkang J. Math., Volume 31 (2000) no. 4, pp. 251-255

[2] O.P. Ahuja; M. Jahangiri Fekete–Szegö problem for a unified class of analytic functions, Panamer. Math. J., Volume 7 (1997) no. 2, pp. 67-78

[3] O. Altintaş; S. Owa Majorizations and quasi-subordinations for certain analytic functions, Proc. Jpn. Acad., Ser. A, Math. Sci., Volume 68 (1992) no. 7, pp. 181-185

[4] N.E. Cho; S. Owa On the Fekete–Szegö problem for strongly α-logarithmic quasiconvex functions, Southeast Asian Bull. Math., Volume 28 (2004) no. 3, pp. 421-430

[5] J.H. Choi; Y.C. Kim; T. Sugawa A general approach to the Fekete–Szegö problem, J. Math. Soc. Jpn., Volume 59 (2007) no. 3, pp. 707-727

[6] M. Darus; D.K. Thomas α-Logarithmically convex functions, Indian J. Pure Appl. Math., Volume 29 (1998) no. 10, pp. 1049-1059

[7] M. Darus; N. Tuneski On the Fekete–Szegö problem for generalized close-to-convex functions, Int. Math. J., Volume 4 (2003) no. 6, pp. 561-568

[8] M. Haji Mohd; M. Darus Fekete–Szegö problems for quasi-subordination classes, Abstr. Appl. Anal., Volume 2012 (2012), p. 192956 (14 p)

[9] F.R. Keogh; E.P. Merkes A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., Volume 20 (1969), pp. 8-12

[10] S.Y. Lee Quasi-subordinate functions and coefficient conjectures, J. Korean Math. Soc., Volume 12 (1975) no. 1, pp. 43-50

[11] Z. Lewandowski; S. Miller; E. Złotkiewicz γ-Starlike functions, Ann. Univ. Mariae Curie-Skłodowska, Sect. A, Volume 28 (1976), pp. 53-58

[12] W. Ma; D. Minda A unified treatment of some special classes of univalent functions, Tianjin, China, 1992 (Conf. Proc. Lecture Notes Anal., I), Int. Press, Cambridge, MA, USA (1994), pp. 157-169

[13] F.Y. Ren; S. Owa; S. Fukui Some inequalities on quasi-subordinate functions, Bull. Aust. Math. Soc., Volume 43 (1991) no. 2, pp. 317-324

[14] M.S. Robertson Quasi-subordination and coefficient conjectures, Bull. Amer. Math. Soc., Volume 76 (1970), pp. 1-9

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