On Certain Subclasses of Analytic Functions Associated with a Symmetric q -Differential Operator

Vasile-Aurel Caus
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Vasile-Aurel Caus: Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania

Mathematics, 2025, vol. 13, issue 17, 1-23

Abstract: This paper explores a class of analytic functions defined in the open unit disk by means of a symmetric q -differential operator. In the first part, we derive sufficient conditions for functions to belong to a subclass associated with this operator, using inequalities involving their coefficients. Additionally, we establish several inclusion relations between these subclasses, obtained by varying the defining parameters. In the second part, we focus on differential subordination and superordination for functions transformed by the operator. We provide sufficient conditions under which such functions are subordinate or superordinate to univalent functions, and we determine the best dominant and best subordinant in specific cases. These results are complemented by several corollaries that highlight particular instances of the main theorems. Furthermore, we present a sandwich-type result that brings together the subordination and superordination frameworks in a unified analytic statement.

Keywords: analytic functions; multivalent functions; symmetric q -calculus; symmetric q -differential operator; differential subordination; differential superordination (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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