Fekete-szegö results for certain class of meromorphic functions using $$q-$$derivative operator

In the present paper, we introduce the subclasses $$\sum _{b}^{*}\left( q,\phi \right) $$ ∑ b ∗ q , ϕ and $$\sum _{b}^{*}\left( \alpha ,q,\phi \right) $$ ∑ b ∗ α , q , ϕ of meromorphic functions $$f\left( z\right) $$ f z satisfying $$1+\frac{1}{b}\left[ -\frac{qzD_{q}^{*}f(z)}{f(z)}-1\right] \prec \phi (z)$$ 1 + 1 b - q z D q ∗ f ( z ) f ( z ) - 1 ≺ ϕ ( z ) and $$1+\frac{1}{b}\left[ \frac{-\left( 1-\frac{\alpha }{q}\right) qzD_{q}^{*}f\left( z\right) +\alpha qzD_{q}^{*}\left[ zD_{q}^{*}f\left( z\right) \right] }{\left( 1-\frac{\alpha }{q}\right) f\left( z\right) -\alpha zD_{q}^{*}f\left( z\right) }-1\right] \prec \phi (z)\ (b\in \mathbb {C} ^{*}=\mathbb {C}\backslash \left\{ 0\right\} ,\ $$ 1 + 1 b - 1 - α q q z D q ∗ f z + α q z D q ∗ z D q ∗ f z 1 - α q f z - α z D q ∗ f z - 1 ≺ ϕ ( z ) ( b ∈ C ∗ = C \ 0 , $$\alpha \in \mathbb {C}\backslash (0,1],\ \operatorname {Re}(\alpha )\ge 0,\ 0<q<1)$$ α ∈ C \ ( 0 , 1 ] , Re ( α ) ≥ 0 , 0 < q < 1 ) , respectively. Sharp bounds for the Fekete-Szegö functional $$\left| a_{1}-\mu a_{0}^{2}\right| $$ a 1 - μ a 0 2 are obtained.