Subordination Results for the Second-Order Differential Polynomials of Meromorphic Functions

Abstract

The outcome of the research presented in this paper is the definition and investigation of two new subclasses of meromorphic functions. The new subclasses are introduced using a differential operator defined considering second-order differential polynomials of meromorphic functions in U\{0}=z∈C:0<z<1. The investigation of the two new subclasses leads to establishing inclusion relations and the proof of convexity and convolution properties regarding each of the two subclasses. Further, involving the concept of subordination, the Fekete–Szegö problem is also discussed for the aforementioned subclasses. Symmetry properties derive from the use of the convolution and from the convexity proved for the new subclasses of functions.