Coefficient estimates for certain subclass of meromorphic and bi-univalent functions

Abstract

In this paper, we introduce and investigate an interesting subclass of meromorphic and bi-univalent functions on Δ={z∈C :1 <|z|<∞}. Furthermore, for functions belonging to this class, estimates on the initial coefficients are obtained. The results presented in this paper would generalize and improve some recent works of several earlier authors.

Keywords

• Bi-univalent functions,meromorphic functions,meromorphic bi-univalent functions,coefficient estimates

References

1. Duren, P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
2. Halim, S. A., Hamidi S. G. and Ravichandran, V., Coefficient estimates for mero- morphic bi-univalent functions, arXiv:1108.4089v1 (2011), 1-9.
3. Kubota, Y., Coefficients of meromorphic univalent functions, Kodai Math. Sem. Rep. 28(2-3) (1976/77), 253-261.
4. Orhan, H., Magesh N. and Balaji, V. K., Initial coefficient bounds for certain classes of meromorphic bi-univalent functions, Asian European J. Math. 7(1) (2014), 1-9.
5. Schiffer, M., Surun probleme dextremum de la representation conforme, Bull. Soc. Math. France 66 (1938), 48-55.
6. Schober, G., Coefficients of inverses of meromorphic univalent functions, Proc. Amer. Math. Soc. 67(1) (1977), 111-116.
7. Springer, G., The coefficient problem for Schlicht mappings of the exterior of the unit circle, Trans. Amer. Math. Soc. 70 (1951), 421-450.