SavedAdd your journal

Journals / New Trends in Mathematical Sciences / 2016 / Cilt: 4 Sayı: 3

Coefficient bounds for new subclasses of bi-univalent functions

Bilal SEKER
Veysi MEHMETOGLU
Pages
197–203
Publication Date
2016-09-30
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Presented results are a generalization of the results obtained by Srivastava et al.[12], Frasin and Aouf [7] and Çağlar et al.[5].

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, introduction of new subclasses of bi-univalent functions in the open disk was defined.
📊
Key Findings & Data:Moreover,by using Salagean operator,in these new subclasses for functions, upper bounds for the second and third coefficients were found.
💡
Conclusion & Impact:Presented results are a generalization of the results obtained by Srivastava et al.[12], Frasin and Aouf [7] and Çağlar et al.[5].
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Univalent functions · bi-univalent functions · coefficient bounds

Abstract

In the present paper, introduction of new subclasses of bi-univalent functions in the open disk was defined. Moreover,by using Salagean operator,in these new subclasses for functions, upper bounds for the second and third coefficients were found. Presented results are a generalization of the results obtained by Srivastava et al.[12], Frasin and Aouf [7] and Çağlar et al.[5].

🔖

Cite This Article

SEKER, B., MEHMETOGLU, V. (2016). Coefficient bounds for new subclasses of bi-univalent functions. New Trends in Mathematical Sciences, Cilt: 4 Sayı: 3, 197–203. https://ajindex.com/articles/1003834

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. Altankaya Ş., Yalçın S., Faber polynomial coefficient bounds for a subclass of bi-univalent functions, Stud. Univ. Babeş-Bolyai Math. 61 (1) (2016) 37-44.
  2. Altankaya Ş., Yalçın S., Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I 353 (12) (2015) 1075-1080.
  3. Ali R.M., Lee S.K., Ravichandran V., Supramaniam S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Applied Mathematics Letters, 25 (2012) 344-351.
  4. Brannan D.A., Taha T.S., On some classes of bi-univalent functions, in: S.M. Mazhar, A. Hamoui, N.S. Faour (Eds.), Mathematical Analysis and Its Applications, Kuwait; February 18-21, 1985, in: KFAS Proceedings Series, vol. 3, Pergamon Press,
  5. Elsevier Science Limited, Oxford, 1988, pp. 53-60. See also Studia Univ. Babeş-Bolyai Math. 31 (2) (1986) 70-77.
  6. Çağlar M., Orhan H. and Yağmur N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27(7) (2013),1165-1171.
  7. Duren P.L., Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
  8. Frasin B.A. and Aouf M.K., New subclasses of bi-univalent functions, Applied Mathematics Letters, 24 (2011), 1569-1573.
  9. Lewin M., On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967) 63-68.
  10. Netanyahu E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z| Salagean G.S., Subclasses of univalent functions, Lecture Notes in Math., Springer, Berlin, 1013, 362-372, 1983.
  11. Srivastava H. M., Bulut S., Çağlar M., and Yağmur N., a Coefficient estimates for a general subclass of analytic and biunivalent functions, a Filomat, vol. 27, no. 5, pp.831-842, 2013.
  12. Srivastava H.M., Mishra A.K. and Gochhayat P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010) 1188-1192.
  13. Srivastava H.M., Sümer Eker S., Ali RM., Coefficient bounds for a certain class of analytic and bi-univalent functions. Filomat 29 (2015) 1839-1845.
  14. Taha T.S., Topics in Univalent Function Theory, Ph.D. Thesis, University of London, 1981.