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Applications of q -Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses

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  • Ekram E. Ali

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
    Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said 42521, Egypt)

  • Georgia Irina Oros

    (Department of Mathematics, University of Oradea, Universitatii 1, 410087 Oradea, Romania)

  • Shujaat Ali Shah

    (Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology (QUEST), Nawabshah 67450, Pakistan)

  • Abeer M. Albalahi

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia)

Abstract

In this article, a new linear extended multiplier operator is defined utilizing the q -Choi–Saigo–Srivastava operator and the q -derivative. Two generalized subclasses of q —uniformly convex and starlike functions of order δ —are defined and studied using this new operator. Necessary conditions are derived for functions to belong in each of the two subclasses, and subordination theorems involving the Hadamard product of such particular functions are stated and proven. As applications of those findings using specific values for the parameters of the new subclasses, associated corollaries are provided. Additionally, examples are created to demonstrate the conclusions’ applicability in relation to the functions from the newly introduced subclasses.

Suggested Citation

  • Ekram E. Ali & Georgia Irina Oros & Shujaat Ali Shah & Abeer M. Albalahi, 2023. "Applications of q -Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2705-:d:1171268
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    References listed on IDEAS

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    1. Alina Alb Lupaş & Georgia Irina Oros, 2022. "Fuzzy Differential Subordination and Superordination Results Involving the q -Hypergeometric Function and Fractional Calculus Aspects," Mathematics, MDPI, vol. 10(21), pages 1-11, November.
    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. Ekram Elsayed Ali & Teodor Bulboacă, 2020. "Subclasses of Multivalent Analytic Functions Associated with a q -Difference Operator," Mathematics, MDPI, vol. 8(12), pages 1-8, December.
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