In this paper, we find coefficient estimates by a new method making use of the Faber polynomial expansions for a comprehensive subclass of analytic bi-univalent functions, which is defined by subordinations in the open unit disk. The coefficient bounds presented in this paper would generalize and improve some recent works appeared in the literature.
In this paper, we use the Faber polynomial expansion to find upper bounds for |an| (n ≥ 3) coefficients of functions belong to classes
$\begin{array}{}
H_{q}^{\Sigma}(\lambda,h),\, ST_{q}^{\Sigma}(\alpha,h)\,\text{ and} \,\,M_{q}^{\Sigma}(\alpha,h)
\end{array}$ which are defined by quasi-subordinations in the open unit disk đť•Ś. Further, we generalize some of the previously published results.
In this work, we introduce and investigate a subclass Hh,p ?m(?,?) of
analytic and bi-univalent functions when both f(z) and f-1(z) are m-fold
symmetric in the open unit disk U. Moreover, we find upper bounds for the
initial coefficients |am+1| and |a2m+1| for functions belonging to this
subclass Hh,p ?m(?,?). The results presented in this paper would generalize
and improve those that were given in several recent works.
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