Some subclasses of meromorphically multivalent functions associated with a linear operator

Let ΣpΣp denote the class of functions normalized byf(z)=z-p+∑n=1∞anzn-p(p∈N:={1,2,3,…}),which are analytic and p  -valent in 0<|z|<10<|z|<1. Making use of a linear operator, which is defined here by means of the Hadamard product (or convolution), we introduce some new subclasses of the meromorphically p  -valent function class ΣpΣp and investigate their inclusion relationships and convolution properties. Some integral-preserving properties are also considered.