Let 𝒜 be the class of normalized functions which are analytic in the open unit disc. Jakson q-derivative represented by convolution operator

$${D}_{q}f\left(z\right)=\frac{1}{z}\left\{f\left(z\right)\u2605\frac{z}{\left(1-qz\right)\left(1z\right)}\right\},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}f\in \mathcal{A},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}q\in \left(0,1\right)$$
{D_q}f\left( z \right) = {1 \over z}\left\{ {f\left( z \right)\star{z \over {\left( {1 - qz} \right)\left( {1z} \right)}}} \right\},\,\,\,\,f \in \mathcal{A},\,\,\,q \in \left( {0,1} \right)
is used to introduce a unified class M_{q}(α, β, γ), α ≥ 0, β, γ ∈ [0, 1) and its various mapping properties are studied. For q → 1^{−1}, β = γ = 0 and α = 1, this class reduces to the class K of close-to-convex univalent functions. A number of interesting results such as q-Bernardi integral operator and inclusion relations are included as part of this study. Applications are also pointed out as consequences of the main results.