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

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.

Properties of Meromorphic Spiral-Like Functions Associated with Symmetric Functions

“…For details pertaining to the significance of univalent function theory in dual with quantum calculus, refer to [21,22] (also see [23][24][25][26]). Meromorphic multivalent functions have been extensively studied by various authors, but motivation and references of this study are [1,13,[27][28][29][30][31][32][33][34][35][36].…”

Integral Operators Applied to Classes of Convex and Close-to-Convex Meromorphic p-Valent Functions

“…Some twenty years later, S. S. Miller and P. T. Mocanu revealed the theory of differential subordinations with the very useful method of admissible functions, and many authors returned to the study of meromorphic functions, as we can see from works [3][4][5][6]. Nowadays, although the class of meromorphic functions is not as used as other classes of functions, there are many recent papers that have dealt with its properties (see [7][8][9][10]).…”