## Coefficient estimates for a class of meromorphic bi-univalent functions. (Estimation de coefficients pour une classe de functions méromorphes bi-univalentes.)(English. French summary)Zbl 1283.30026

Let $$\Sigma$$ denote the family of meromorphic functions $$g$$ of the form $g(z)= z+b_0+\sum_{n=1}^\infty b_n z^{-n}$ that are univalent in $$\Delta = \{z:\;1 < |z|<\infty\}$$. For $$0\leq \alpha <1, \lambda \geq 1$$, let $$B\Sigma(\alpha;\lambda)$$ be a subclass of $$\Sigma$$, consisting of functions $$g$$ such that $\mathrm{Re}\left\{(1-\lambda)\frac{g(z)}{z}+\lambda\, g'(z)\right\}>\alpha\quad \text{and}\quad \mathrm{Re}\left\{(1-\lambda)\frac{h(w)}{w}+\lambda\, h'(w)\right\} >\alpha\quad (z, w \in \Delta),$ where $$h$$ is the inverse map of $$g$$. The family $$B\Sigma(\alpha;\lambda)$$ is called meromorphic bi-univalent class of functions. Applying Faber polynomials a coefficient problem for $$g\in \Sigma(\alpha;\lambda)$$ is solved.

### MSC:

 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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### References:

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