호남수학학술지 (Honam Mathematical Journal)

  • 제39권4호
  • /
  • Pages.591-601
  • /
  • 2017
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

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)
  • 투고 : 2017.07.31
  • 심사 : 2017.10.19
  • 발행 : 2017.12.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  1. 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.
  2. S. Altinkaya and S. Yalcin, Coefficient estimates for a certain subclass of biunivalent functions, Matematiche 71(2) (2016), 53-61.
  3. D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math. 31(2) (1986), 70-77.
  4. S. Bulut, Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math. 43(2) (2013), 59-65.
  5. 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.
  6. 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.
  7. M. Caglar, H. Orhan and N. Yagmur, Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27(7) (2013), 1165-1171. https://doi.org/10.2298/FIL1307165C
  8. E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal. 2(1) (2013), 49-60.
  9. P. L. Duren, Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer, New York, 1983.
  10. B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569-1573. https://doi.org/10.1016/j.aml.2011.03.048
  11. 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.
  12. B. Seker, On a new subclass of bi-univalent functions defined by using Salagean operator, Turkish J. Math., accepted.
  13. 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. https://doi.org/10.2298/FIL1305831S
  14. H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188-1192. https://doi.org/10.1016/j.aml.2010.05.009
  15. 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. https://doi.org/10.1016/j.aml.2011.11.013
  16. P. Zaprawa, Estimates of initial coecients for bi-univalent functions, Abstr. Appl. Anal. 2014, Art. ID 357480, 6 pp.
  17. P. Zaprawa, On the Fekete-Szego problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin 21(1) (2014), 169-178.