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Subclasses of Multivalent Analytic Functions Associated with a q -Difference Operator

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  • Ekram Elsayed Ali

    (Department of Mathematics, Faculty 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
    These authors contributed equally to this work.)

  • Teodor Bulboacă

    (Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

Abstract

In this article we introduced and studied some inclusion properties for new subclasses of multivalent analytic functions defined by using the q -derivative operator. With the aid of the Jackson q -derivative we defined two new operators that generalize many other previously studied operators, and help us to define two new subclasses of functions with several interesting properties studied in this paper. The methods used for the proof of our results are special tools of the differential subordination theory of one-variable functions.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2184-:d:458752
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    References listed on IDEAS

    as
    1. Miraj Ul-Haq & Mohsan Raza & Muhammad Arif & Qaiser Khan & Huo Tang, 2019. "q-Analogue of Differential Subordinations," Mathematics, MDPI, vol. 7(8), pages 1-16, August.
    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.
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    Cited by:

    1. 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.
    2. Georgia Irina Oros & Gheorghe Oros & Shigeyoshi Owa, 2022. "Applications of Certain p -Valently Analytic Functions," Mathematics, MDPI, vol. 10(6), pages 1-17, March.

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