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Applications of Some Subclasses of Meromorphic Functions Associated with the q -Derivatives of the q -Binomials

Author

Listed:
  • Ekram E. 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)

  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan)

  • Abdel Moneim Y. Lashin

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Abeer M. Albalahi

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

Abstract

In this article, we make use of the q -binomial theorem to introduce and study two new subclasses ℵ ( α q , q ) and ℵ ( α , q ) of meromorphic functions in the open unit disk U , that is, analytic functions in the punctured unit disk U ∗ = U \ { 0 } = { z : z ∈ C and 0 < z < 1 } . We derive inclusion relations and investigate an integral operator that preserves functions which belong to these function classes. In addition, we establish a strict inequality involving a certain linear convolution operator which we introduce in this article. Several special cases and corollaries of our main results are also considered.

Suggested Citation

  • Ekram E. Ali & Hari M. Srivastava & Abdel Moneim Y. Lashin & Abeer M. Albalahi, 2023. "Applications of Some Subclasses of Meromorphic Functions Associated with the q -Derivatives of the q -Binomials," Mathematics, MDPI, vol. 11(11), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2496-:d:1158445
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