Subordinations Results on a q -Derivative Differential Operator

Loriana Andrei () and Vasile-Aurel Caus
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Loriana Andrei: Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania
Vasile-Aurel Caus: Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania

Mathematics, 2024, vol. 12, issue 2, 1-20

Abstract: In this research paper, we utilize the q -derivative concept to formulate specific differential and integral operators denoted as R q n , m , λ , F q n , m , λ and G q n , m , λ . These operators are introduced with the aim of generalizing the class of Ruscheweyh operators within the set of univalent functions. We extract certain properties and characteristics of the set of differential subordinations employing specific techniques. By utilizing the newly defined operators, this paper goes on to establish subclasses of analytic functions defined on an open unit disc. Additionally, we delve into the convexity properties of the two recently introduced q -integral operators, F q n , m , λ and G q n , m , λ . Special cases of the primary findings are also discussed.

Keywords: analytic functions; q -derivative; subordinations; q -convex functions; Ruscheweyh derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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