[La fonctionnelle de Fekete–Szegö associée aux transformations racine utilisant la subordination]
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.
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.
Accepté le :
Publié le :
@article{CRMATH_2015__353_7_617_0,
author = {Gurusamy, Palpandy and Sok\'o{\l}, Janusz and Sivasubramanian, Srikandan},
title = {The {Fekete{\textendash}Szeg\"o} functional associated with \protect\emph{k}-th root transformation using quasi-subordination},
journal = {Comptes Rendus. Math\'ematique},
pages = {617--622},
publisher = {Elsevier},
volume = {353},
number = {7},
year = {2015},
doi = {10.1016/j.crma.2015.03.016},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.03.016/}
}
TY - JOUR AU - Gurusamy, Palpandy AU - Sokół, Janusz AU - Sivasubramanian, Srikandan TI - The Fekete–Szegö functional associated with k-th root transformation using quasi-subordination JO - Comptes Rendus. Mathématique PY - 2015 SP - 617 EP - 622 VL - 353 IS - 7 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.03.016/ DO - 10.1016/j.crma.2015.03.016 LA - en ID - CRMATH_2015__353_7_617_0 ER -
%0 Journal Article %A Gurusamy, Palpandy %A Sokół, Janusz %A Sivasubramanian, Srikandan %T The Fekete–Szegö functional associated with k-th root transformation using quasi-subordination %J Comptes Rendus. Mathématique %D 2015 %P 617-622 %V 353 %N 7 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.03.016/ %R 10.1016/j.crma.2015.03.016 %G en %F CRMATH_2015__353_7_617_0
Gurusamy, Palpandy; Sokół, Janusz; Sivasubramanian, Srikandan. The Fekete–Szegö functional associated with k-th root transformation using quasi-subordination. Comptes Rendus. Mathématique, Tome 353 (2015) no. 7, pp. 617-622. doi : 10.1016/j.crma.2015.03.016. http://www.numdam.org/articles/10.1016/j.crma.2015.03.016/
[1] On the Fekete–Szegö problem for alpha-quasi-convex functions, Tamkang J. Math., Volume 31 (2000) no. 4, pp. 251-255
[2] Fekete–Szegö problem for a unified class of analytic functions, Panamer. Math. J., Volume 7 (1997) no. 2, pp. 67-78
[3] Majorizations and quasi-subordinations for certain analytic functions, Proc. Jpn. Acad., Ser. A, Math. Sci., Volume 68 (1992) no. 7, pp. 181-185
[4] On the Fekete–Szegö problem for strongly α-logarithmic quasiconvex functions, Southeast Asian Bull. Math., Volume 28 (2004) no. 3, pp. 421-430
[5] A general approach to the Fekete–Szegö problem, J. Math. Soc. Jpn., Volume 59 (2007) no. 3, pp. 707-727
[6] α-Logarithmically convex functions, Indian J. Pure Appl. Math., Volume 29 (1998) no. 10, pp. 1049-1059
[7] On the Fekete–Szegö problem for generalized close-to-convex functions, Int. Math. J., Volume 4 (2003) no. 6, pp. 561-568
[8] Fekete–Szegö problems for quasi-subordination classes, Abstr. Appl. Anal., Volume 2012 (2012), p. 192956 (14 p)
[9] A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., Volume 20 (1969), pp. 8-12
[10] Quasi-subordinate functions and coefficient conjectures, J. Korean Math. Soc., Volume 12 (1975) no. 1, pp. 43-50
[11] γ-Starlike functions, Ann. Univ. Mariae Curie-Skłodowska, Sect. A, Volume 28 (1976), pp. 53-58
[12] 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] Some inequalities on quasi-subordinate functions, Bull. Aust. Math. Soc., Volume 43 (1991) no. 2, pp. 317-324
[14] Quasi-subordination and coefficient conjectures, Bull. Amer. Math. Soc., Volume 76 (1970), pp. 1-9
Cité par Sources :
