Some properties of a Certain family of Meromorphically Univalent Functions defined by an Integral Operator

Abstract

Abstract. Making use of a linear operator, we introduce certain subclass of meromorphically univalent functions in the punctured unit disk and study its properties including some inclusion results, coefficient and distortion problems. Our result generalize many results known in the literature.

Subordination and inclusion theorems for subclasses of meromorphic functions with applications to electromagnetic cloaking

“…(i) for n = 1, m = 0, p = 1 and α = 0, the class M 1,0 λ,1 (a, c; 0; A, B) := M λ (a, c; A, B) has been studied in [6], (ii) for n = 1, m = 0, the class M 1,0 λ,p (a, c; α; A, B) is a special case (for q = 2, s = 1), of a class studied in [22], In the present paper, in Section 3, we find several inclusion theorems for the class M …”

On Certain Subclasses of Meromorphic Functions with Positive Coefficients involving Generalized Liu-Srivastava Operator

“…was introduced and studied by Liu and Srivastava [14] (see also [1], [11] and [25]). Further,we remark in passing that this operator L[α 1 ; β 1 ] is closely related to the Carlson-Shaffer operator L[α 1 ; β 1 ] defined on the space of analytic and univalent functions in U.…”

Argument estimates of certain meromorphically p-valent functions associated with a family of linear operator

“…Let Σ p denote the class of functions f (z) of the form: 1) which are analytic and p-valent in the punctured open unit disc U * = {z ∈ C : 0 < |z| < 1}. If f (z) and g(z) are analytic in U = U * ∪ {0}, we say that f (z) is subordinate to g(z), written f ≺ g or f (z) ≺ g(z) (z ∈ U ), if there exists a Schwarz function w(z) in U , with w(0) = 0 and |w(z)| < 1 (z ∈ U ), such that f (z) = g(w(z)), (z ∈ U ).…”