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Subordinations Results on a q -Derivative Differential Operator

Author

Listed:
  • Loriana Andrei

    (Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania
    These authors contributed equally to this work.)

  • Vasile-Aurel Caus

    (Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Loriana Andrei & Vasile-Aurel Caus, 2024. "Subordinations Results on a q -Derivative Differential Operator," Mathematics, MDPI, vol. 12(2), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:208-:d:1315184
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    References listed on IDEAS

    as
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    2. F. M. Al-Oboudi, 2004. "On univalent functions defined by a generalized Sălăgean operator," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-8, January.
    3. Hari M. Srivastava & Qazi Zahoor Ahmad & Nasir Khan & Nazar Khan & Bilal Khan, 2019. "Hankel and Toeplitz Determinants for a Subclass of q -Starlike Functions Associated with a General Conic Domain," Mathematics, MDPI, vol. 7(2), pages 1-15, February.
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