Inclusion properties for analytic functions of $q$-analogue multiplier-Ruscheweyh operator

The results of this work have a connection with the geometric function theory and they were obtained using methods based on subordination along with information on $\mathfrak{q}$-calculus operators. We defined the $\mathfrak{q}$-analogue of multiplier- Ruscheweyh operator of a certain family of linear operators $I_{\mathfrak{q},\mu }^s(\lambda ,\ell )\mathfrak{f}(\varsigma )(s\in {\mathbb{N}}_0=\mathbb{N}\cup \{0\},\mathbb{N}=\left\{1,2,3,..\right\};\ell ,\lambda ,\mu \ge 0,0<\mathfrak{q}<1)$. Our major goal was to build some analytic function subclasses using $I_{\mathfrak{q},\mu }^s(\lambda ,\ell )\mathfrak{f}(\varsigma )$ and to look into various inclusion relationships that have integral preservation features.