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Some applications of subordination theorems associated with fractional \(q\)-calculus operator. (English) Zbl 07729569

Summary: Using the operator \(\mathfrak{D}_{q,\varrho}^{m}(\lambda,l)\), we introduce the subclasses \(\mathfrak{Y}^{*m}_{q,\varrho}(l,\lambda,\gamma)\) and \(\mathfrak{K}^{*m}_{q,\varrho}(l,\lambda,\gamma)\) 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.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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