A generalization of multivalent functions with negative coefficients (Q1123284)

Let \(T_ p\) be the class of analytic and p-valent functions which can be expressed in the form \[ f(z)=z^ p-\sum^{\infty}_{n=1}| a_{n+p}| z^{n+p},\quad | z| <1,\quad p=1,2,.... \] The author studies various subclasses of \(T_ p\). Sharp results concerning coefficient estimates, distortion and covering theorems are obtained. Some closure properties under arithmetic mean and convex linear combinations are also obtained.