Mathematica Bohemica, first online, pp. 1-18


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

Wafaa Y. Kota, Rabha Mohamed El-Ashwah

Received April 16, 2021.   Published online May 2, 2022.

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
Classification MSC:  30C45, 30C50
DOI:  10.21136/MB.2022.0047-21

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Affiliations:   Wafaa Y. Kota, Rabha Mohamed El-Ashwah, Department of Mathematics, Faculty of Science, Damietta University, New Damietta, 34511, Egypt, e-mail: wafaa_kota@yahoo.com, r_elashwah@yahoo.com


 
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