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

Abstract

a b s t r a c tIn this paper subordination and inclusion relations are studied for some subclasses of multivalent meromorphic functions in the punctured unit disc having a pole of order p at the origin. The subclasses under investigation are defined through combinations and iterations of a meromorphic analogue of the Cho-Kwon-Srivastava operator for normalized analytic functions. Specially, emphasis is given in this study on the effect of the increase of different parameters on the size of the subclasses. Applications are indicated for the subordination results to electromagnetic cloaking.

Certain Families of Multivalent Analytic Functions Associated with Iterations of the Owa-Srivastava Fractional Differintegral Operator

“…Their work generalized several earlier results of Srivastava and Mishra [13]. This theme has been further pursued in our more recent papers [6,14,15]. In the sequel to Journal of Complex Analysis 3 these current investigations, in the present paper, we define the following subclass of A associated with the iterated operator D ( , ) ( , ) and investigate its several interesting properties.…”

“…if condition (15) holds for some Schwarz function ( ) (see [12] for details). We also need the following definition of Hadamard product (or convolution).…”

Some Sufficient Conditions for Starlikeness and Convexity of Order

“…Very recently, Mishra et al [18] have given some applications of subordination relationship (40) to electromagnetic cloaking. In the present paper, we found several sufficient conditions under which relationship of the form (40) holds for functions which are more general than circular maps.…”

Sandwich results for subclasses of multivalent meromorphic functions associated with iterations of the Cho-Kwon-Srivastava transform

“…Recently, Mishra et al [28] introduced and obtained subordination results of multivalent meromorphic functions defined by using the Carlson-Shaffer operator [13] and iterations of a meromorphic analogue of the Cho-Kwon-Srivastava operator [15] (see also [21,22,37]) and its combinations.…”