Admissible Classes of Multivalent Meromorphic Functions Defined by a Linear Operator

Abstract

The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on differential subordination, one of the newest techniques used in the field, also known as the technique of admissible functions. For that, the appropriate classes of admissible functions are first defined. Based on these classes, we obtain some differential subordination and superordination results for multivalent meromorphic functions, analytic in the punctured unit disc, related to a linear operator ℑρ,τp(ν), for τ>0,ν,ρ∈C, such that Re(ρ−ν)≧0, Re(ν)>τp,(p∈N). Moreover, taking into account both subordination and superordination results, we derive a sandwich-type theorem. The connection with some other known results and an example are also provided.

Keywords

• analytic function
• meromorphic univalent function
• differential subordination
• differential superordination
• sandwich-type
• admissible class