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Subclasses of Multivalent Meromorphic Functions with a Pole of Order p at the Origin

Author

Listed:
  • Daniel Breaz

    (Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
    These authors contributed equally to this work.)

  • Kadhavoor R. Karthikeyan

    (Department of Applied Mathematics and Science, National University of Science & Technology, Muscat P.O. Box 620, Oman
    These authors contributed equally to this work.)

  • Elangho Umadevi

    (Department of Mathematics and Statistics, College of Natural and Health Sciences, Zayed University, Abu Dhabi P.O. Box 144534, United Arab Emirates
    These authors contributed equally to this work.)

Abstract

In this paper, we carry out a systematic study to discover the properties of a subclass of meromorphic starlike functions defined using the Mittag–Leffler three-parameter function. Differential operators involving special functions have been very useful in extracting information about the various properties of functions belonging to geometrically defined function classes. Here, we choose the Prabhakar function (or a three parameter Mittag–Leffler function) for our study, since it has several applications in science and engineering problems. To provide our study with more versatility, we define our class by employing a certain pseudo-starlike type analytic characterization quasi-subordinate to a more general function. We provide the conditions to obtain sufficient conditions for meromorphic starlikeness involving quasi-subordination. Our other main results include the solution to the Fekete–Szegő problem and inclusion relationships for functions belonging to the defined function classes. Several consequences of our main results are pointed out.

Suggested Citation

  • Daniel Breaz & Kadhavoor R. Karthikeyan & Elangho Umadevi, 2022. "Subclasses of Multivalent Meromorphic Functions with a Pole of Order p at the Origin," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:600-:d:750393
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    References listed on IDEAS

    as
    1. U. Ayub & S. Mubeen & T. Abdeljawad & G. Rahman & Kottakkaran Sooppy Nisar & Ljubisa Kocinac, 2020. "The New Mittag-Leffler Function and Its Applications," Journal of Mathematics, Hindawi, vol. 2020, pages 1-8, December.
    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. Maisarah Haji Mohd & Maslina Darus, 2012. "Fekete-Szegö Problems for Quasi-Subordination Classes," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, October.
    Full references (including those not matched with items on IDEAS)

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