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Certain Quantum Operator Related to Generalized Mittag–Leffler Function

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  • Mansour F. Yassen

    (Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj 11912, Saudi Arabia
    Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt)

  • Adel A. Attiya

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

In this paper, we present a novel class of analytic functions in the form h ( z ) = z p + ∑ k = p + 1 ∞ a k z k in the unit disk. These functions establish a connection between the extended Mittag–Leffler function and the quantum operator presented in this paper, which is denoted by ℵ q , p n ( L , a , b ) and is also an extension of the Raina function that combines with the Jackson derivative. Through the application of differential subordination methods, essential properties like bounds of coefficients and the Fekete–Szegő problem for this class are derived. Additionally, some results of special cases to this study that were previously studied were also highlighted.

Suggested Citation

  • Mansour F. Yassen & Adel A. Attiya, 2023. "Certain Quantum Operator Related to Generalized Mittag–Leffler Function," Mathematics, MDPI, vol. 11(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4963-:d:1300513
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    References listed on IDEAS

    as
    1. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
    2. Stanisława Kanas, 2003. "Techniques of the differential subordination for domains bounded by conic sections," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-12, January.
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