Applications of Linear Differential Operator on Varying Arguments

In the present work, using Al-Oboudi operator and Carlson-Shaffer operator, we introduce a new Linear operator \(\mathcal{AS}_{\lambda, q}^{\delta}\). The objective is to define the new subclasses of analytic functions \(\mathcal{VS}_{\lambda,\delta}^{\alpha, \beta} (a,c,n; q)\), \(\mathcal{VS}_{\lambda,\delta}^{\alpha}(a,c,n;q) \) using the above linear operator and for functions belonging to these classes we obtain coefficient estimates and many more related properties like extreme points, integral means, unified radii results etc.