Coefficient estimates for a class of meromorphic bi-univalent functions (Q357406)

Let \(\Sigma\) denote the family of meromorphic functions \(g\) of the form NEWLINE\[NEWLINEg(z)= z+b_0+\sum_{n=1}^\infty b_n z^{-n}NEWLINE\]NEWLINE 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 NEWLINE\[NEWLINE\mathrm{Re}\left\{(1-\lambda)\frac{g(z)}{z}+\lambda\, g'(z)\right\}>\alpha\quad \text{and}\quad \mathrm{Re}\left\{(1-\lambda)\frac{h(w)}{w}+\lambda\, h'(w)\right\} >\alpha\quad (z, w \in \Delta),NEWLINE\]NEWLINE 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.