Comptes Rendus
no. 8
Complex analysis
A note on the coefficient estimates of bi-close-to-convex functions

Presented by: the Editorial Board

Zhi-Gang Wang1; Serap Bulut2
1 School of Mathematics and Computing Science, Hunan First Normal University, Changsha 410205, Hunan, PR China
2 Faculty of Aviation and Space Sciences, Kocaeli University, Arslanbey Campus, 41285 Kartepe-Kocaeli, Turkey
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 876-880.

In a recent paper, Hamidi and Jahangiri [C. R. Acad. Sci. Paris, Ser. I 352 (2014) 17–20] introduced and investigated the class of bi-close-to-convex functions, and determined the estimates for the general Taylor–Maclaurin coefficients of the functions therein. This note mainly aims to point out and correct the errors of the main result in the above-mentioned paper.

Hamidi et Jahangiri [C. R. Acad. Sci. Paris, Ser. I 352 (2014) 17–20] ont introduit et étudié la classe des fonctions bi-presque convexes. Ils majorent les coefficients de Taylor–MacLaurin de ces fonctions bi-presque convexes. Toutefois, la note citée ci-dessus contient des erreurs, que nous mettons en évidence et corrigeons ici.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.07.014

Zhi-Gang Wang 1; Serap Bulut 2

1 School of Mathematics and Computing Science, Hunan First Normal University, Changsha 410205, Hunan, PR China
2 Faculty of Aviation and Space Sciences, Kocaeli University, Arslanbey Campus, 41285 Kartepe-Kocaeli, Turkey 
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Zhi-Gang Wang; Serap Bulut. A note on the coefficient estimates of bi-close-to-convex functions. Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 876-880. doi : 10.1016/j.crma.2017.07.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.07.014/

[1] H. Airault; A. Bouali Differential calculus on the Faber polynomials, Bull. Sci. Math., Volume 130 (2006), pp. 179-222

[2] H. Airault; J. Ren An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math., Volume 126 (2002), pp. 343-367

[3] P.L. Duren Univalent Functions, Grundlehren Math. Wiss., vol. 259, Springer, New York, 1983

[4] S.G. Hamidi; J.M. Jahangiri Faber polynomial coefficient estimates for analytic bi-close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I, Volume 352 (2014), pp. 17-20

[5] M.S. Robertson On the theory of univalent functions, Ann. of Math. (1), Volume 37 (1936), pp. 374-408

[6] F.M. Sakar; H.Ö. Güney Coefficient bounds for a new subclass of analytic bi-close-to-convex functions by making use of Faber polynomial expansion, Turk. J. Math., Volume 41 (2017), pp. 888-895

[7] P.G. Todorov On the Faber polynomials of the univalent functions of class Σ, J. Math. Anal. Appl., Volume 162 (1991), pp. 268-276

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