Complex analysis
A note on the coefficient estimates of bi-close-to-convex functions
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
Wang, Zhi-Gang 1; Bulut, Serap 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
@article{CRMATH_2017__355_8_876_0,
     author = {Wang, Zhi-Gang and Bulut, Serap},
     title = {A note on the coefficient estimates of bi-close-to-convex functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {876--880},
     publisher = {Elsevier},
     volume = {355},
     number = {8},
     year = {2017},
     doi = {10.1016/j.crma.2017.07.014},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2017.07.014/}
}
TY  - JOUR
AU  - Wang, Zhi-Gang
AU  - Bulut, Serap
TI  - A note on the coefficient estimates of bi-close-to-convex functions
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 876
EP  - 880
VL  - 355
IS  - 8
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2017.07.014/
DO  - 10.1016/j.crma.2017.07.014
LA  - en
ID  - CRMATH_2017__355_8_876_0
ER  - 
%0 Journal Article
%A Wang, Zhi-Gang
%A Bulut, Serap
%T A note on the coefficient estimates of bi-close-to-convex functions
%J Comptes Rendus. Mathématique
%D 2017
%P 876-880
%V 355
%N 8
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2017.07.014/
%R 10.1016/j.crma.2017.07.014
%G en
%F CRMATH_2017__355_8_876_0
Wang, Zhi-Gang; Bulut, Serap. 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. http://www.numdam.org/articles/10.1016/j.crma.2017.07.014/

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

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

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

[4] Hamidi, S.G.; Jahangiri, J.M. 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] Robertson, M.S. On the theory of univalent functions, Ann. of Math. (1), Volume 37 (1936), pp. 374-408

[6] Sakar, F.M.; Güney, H.Ö. 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] Todorov, P.G. On the Faber polynomials of the univalent functions of class Σ, J. Math. Anal. Appl., Volume 162 (1991), pp. 268-276

Cited by Sources: