New subclasses of meromorphic bi-univalent functions by associated with ‎subordinate

‎In the present paper‎, ‎we define two subclasses \Sigma(\lambda‎, ‎\alpha‎, ‎\beta)‎, ‎\Sigma_{\mathcal C}(\alpha‎, ‎\beta) of meromorphic univalent functions and subclass \Sigma_{{\mathcal B},{\mathcal C}}(\alpha‎, ‎\beta‎, ‎\lambda) of meromorphic bi-univalent functions‎. ‎Furthermore‎, ‎we obtain estimates on the general coefficients |b_n|~(n \ge۱) for functions in the subclasses \Sigma(\lambda‎, ‎\alpha‎, ‎\beta)‎, ‎\Sigma_{\mathcal C}(\alpha‎, ‎\beta) and estimates for the early coefficients of functions in subclass \Sigma_{{\mathcal B},{\mathcal C}}(\alpha‎, ‎\beta‎, ‎\lambda) by associated subordination‎. ‎The results obtained in this paper would generalize and improve those in related works of several earlier authors‎.

Keywords:

Meromorphic univalent functions‎ , ‎Meromorphic bi-univalent functions‎ , ‎Coefficients estimates‎ , ‎Subordinate