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

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.

___

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