A class of analytic functions based on convolution

We introduce a class TSpg(α) of analytic functions with negative coefficients defined by convolution with a fixed analytic function g(z)=z+Σn=2∞bnzn, bn>0, |z|<1. We obtain the coefficient inequality, coefficient estimate, distortion theorem, a convolution result, extreme points and integral representation for functions in the class TSpg(α).