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

Daniel Breaz, Kadhavoor R. Karthikeyan and Elangho Umadevi
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Daniel Breaz: Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
Kadhavoor R. Karthikeyan: Department of Applied Mathematics and Science, National University of Science & Technology, Muscat P.O. Box 620, Oman
Elangho Umadevi: Department of Mathematics and Statistics, College of Natural and Health Sciences, Zayed University, Abu Dhabi P.O. Box 144534, United Arab Emirates

Mathematics, 2022, vol. 10, issue 4, 1-15

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.

Keywords: meromorphic functions; meromorphic starlike and meromorphic convex functions; quasi-subordination; Fekete–Szeg? problem; coefficient inequalities; generalized Mittag–Leffler function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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