Some applications of subordination theorems associated with fractional $q$-calculus operator

Abstract

Using the operator $\frak{D}_{q,\varrho}^m(\lambda,l)$, we introduce the subclasses $\frak{Y}^{*m}_{q,\varrho}(l,\lambda,\gamma)$ and $\frak{K}^{*m}_{q,\varrho}(l,\lambda,\gamma)$ of normalized analytic functions. Among the results investigated for each of these function classes, we derive some subordination results involving the Hadamard product of the associated functions. The interesting consequences of some of these subordination results are also discussed. Also, we derive integral means results for these classes.

Keywords

• analytic function
• subordination principle
• subordinating factor sequence
• hadamard product
• $q$-difference operator
• fractional $q$-calculus operator