On some classes of p-valent functions involving Carlson–Shaffer operator

Abstract

Let A ( p ) , p ∈ N , be a class of functions f : f ( z ) = z p + ∑ k = p + n ∞ a k z k analytic in the open unit disc E. We use Carlson–Shaffer operator for p-valent functions to define and study certain classes of analytic functions. Inclusion results, a radius problem and some other interesting properties are discussed.