Abstract
In this paper, the authors introduce a new subclass of meromorphic q-starlike functions which are associated with the Janowski functions. A characterization of meromorphically q-starlike functions associated with the Janowski functions has been obtained when the coefficients in their Laurent series expansion about the origin are all positive. This leads to a study of coefficient estimates, distortion theorems, partial sums, and the radius of starlikeness estimates for this class. It is seen that the class considered demonstrates, in some respects, properties analogous to those possessed by the corresponding class of univalent analytic functions with negative coefficients.
Highlights
Mahmood et al Journal of Inequalities and ApplicationsSeveral different subclasses of meromorphic univalent function class M were introduced and studied analogously by the many authors; see, for example, [3, 4, 6, 19, 21]
4 Partial sums for the function class MS∗q[A, B] we examine the ratio of a function of the form (1.5) to its sequence of partial sums
6 Concluding remarks and observations In our present investigation, we have introduced and studied systematically a new subclass of the class of the meromorphically q-starlike functions, which is associated with the Janowski functions
Summary
Several different subclasses of meromorphic univalent function class M were introduced and studied analogously by the many authors; see, for example, [3, 4, 6, 19, 21]. Analogous to Definition 2, we extend the idea of q-difference operator to a function f given by (1.5) from the class M and define analogous of meromorphic analogy of the function class Sq∗[A, B]. ∗, where MS∗ is the well-known function class of meromorphic starlike functions This function class and similar other classes have been extensively studied by Pommerenke [13], Clunie [5], Miller [12], Royster [14], and others.
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