On Classes of Meromorphic Functions Defined by Subordination and Convolution

Abstract

For p∈N*, let Σp denote the class of meromorphic p-valent functions. We consider an operator for meromorphic functions denoted by Tbn, which generalizes some previously studied operators. We introduce some new subclasses of the class Σp, associated with subordination using the above operator, and we prove that these classes are preserved regarding the operator Jp,γ, so we have symmetry when we look at the form of the class in which we consider the function g and at the form of the class of the image Jp,γ(g), where Jp,γ(g)(z)=γ−pzγ∫0zg(t)tγ−1dt, γ∈C with Reγ>p.