Basic Properties for Certain Subclasses of Meromorphic <i>p</i>-Valent Functions with Connected <i>q</i>-Analogue of Linear Differential Operator

Abstract

In this paper, we define three subclasses Mp,αn,q(η,A,B),Ip,αn(λ,μ,γ),, Rpn,q(λ,μ,γ) connected with a q-analogue of linear differential operator Dα,p,Gn,q which consist of functions F of the form F(ζ)=ζ−p+∑j=1−p∞ajζj(p∈N) satisfying the subordination condition p−1ηζDα,p,Gn,qF(ζ)′Dα,p,Gn,qF(ζ)+p≺p1+Aζ1+Bζ.Also, we study the various properties and characteristics of this subclass Mp,αn,q,∗(η,A,B) such as coefficients estimate, distortion bounds and convex family. Also the concept of δneighborhoods and partial sums of analytic functions to the class Mp,αn,q(η,A,B).

Keywords

• fractional derivative
• convolution
• meromorphic function
• q-nalogue of linear differential operator
• complex order
• q-starlike