Coefficient bounds for new subclasses of bi-univalent functions

Year 2016, Volume: 4 Issue: 3, 197 - 203, 30.09.2016

Bilal Seker Veysi Mehmetoglu

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].

Keywords

Univalent functions, bi-univalent functions, coefficient bounds, coefficient estimates

References

• 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.
• 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.
• 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.
• 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, Elsevier Science Limited, Oxford, 1988, pp. 53-60. See also Studia Univ. Babeş-Bolyai Math. 31 (2) (1986) 70-77.
• Çağlar M., Orhan H. and Yağmur N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27(7) (2013),1165-1171.
• Duren P.L., Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
• Frasin B.A. and Aouf M.K., New subclasses of bi-univalent functions, Applied Mathematics Letters, 24 (2011), 1569-1573.
• Lewin M. , On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967) 63-68.
• Netanyahu E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1, Arch. Rational Mech. Anal. 32 (1969) 100-112.
• Salagean G.S., Subclasses of univalent functions, Lecture Notes in Math., Springer, Berlin, 1013, 362-372, 1983.
• 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.
• Srivastava H.M., Mishra A.K. and Gochhayat P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010) 1188-1192.
• 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.
• Taha T.S., Topics in Univalent Function Theory, Ph.D. Thesis, University of London, 1981.