Browse > Article
http://dx.doi.org/10.5831/HMJ.2017.39.4.591

FEKETE-SZEGÖ INEQUALITIES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS DEFINED BY SĂLĂGEAN OPERATOR  

BULUT, Serap (Faculty of Aviation and Space Sciences, Kocaeli University, Arslanbey Campus)
Publication Information
Honam Mathematical Journal / v.39, no.4, 2017 , pp. 591-601 More about this Journal
Abstract
In this paper, by means of the $S{\breve{a}}l{\breve{a}}gean$ operator, we introduce a new subclass $\mathcal{B}^{m,n}_{\Sigma}({\gamma};{\varphi})$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$. For functions belonging to this class, we consider Fekete-$Szeg{\ddot{o}}$ inequalities.
Keywords
Analytic functions; Univalent functions; Bi-univalent functions; Coefficient bounds; Subordination; Fekete-$Szeg{\ddot{o}}$ problem; $S{\breve{a}}l{\breve{a}}gean$ operator;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. Bulut, Coefficient estimates for a new subclass of analytic and bi-univalent functions, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 62(2) (2016), 305-311.
2 M. Caglar, H. Orhan and N. Yagmur, Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27(7) (2013), 1165-1171.   DOI
3 E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal. 2(1) (2013), 49-60.
4 P. L. Duren, Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer, New York, 1983.
5 B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569-1573.   DOI
6 G. S. Salagean, Subclasses of univalent functions, Complex Analysis-Fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math., vol. 1013, pp. 362-372, Springer, Berlin, 1983.
7 B. Seker, On a new subclass of bi-univalent functions defined by using Salagean operator, Turkish J. Math., accepted.
8 H. M. Srivastava, S. Bulut, M. Caglar and N. Yagmur, Coecient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27(5) (2013), 831-842.   DOI
9 H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188-1192.   DOI
10 Q.-H. Xu, Y.-C. Gui and H. M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25 (2012), 990-994.   DOI
11 P. Zaprawa, Estimates of initial coecients for bi-univalent functions, Abstr. Appl. Anal. 2014, Art. ID 357480, 6 pp.
12 S. Bulut, Coefficient estimates for new subclasses of analytic and bi-univalent functions defined by Al-Oboudi differential operator, J. Funct. Spaces Appl. 2013, Art. ID 181932, 7 pp.
13 P. Zaprawa, On the Fekete-Szego problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin 21(1) (2014), 169-178.
14 S. Altinkaya and S. Yalcin, On a new subclass of bi-univalent functions of Sakaguchi type satisfying subordinate conditions, Malaya J. Math. 5(2) (2017), 305-309.
15 S. Altinkaya and S. Yalcin, Coefficient estimates for a certain subclass of biunivalent functions, Matematiche 71(2) (2016), 53-61.
16 D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math. 31(2) (1986), 70-77.
17 S. Bulut, Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math. 43(2) (2013), 59-65.