On certain classes of p-valent analytic functions

Abstract

The objective of the present paper is to introduce a certain general class P(p,α,β)(p∈N={1,2,3,…}, 0≤α<p  and  β≥0) of p-valent analytic functions in the open unit disk U and we prove that if f∈P(p,α,β) then Jp,c(f), defined by Jp,c(f)=c+pzc∫0ztc−1f(t)dt    (c∈N) belongs to P(p,α,β). We also investigate inclusion properties of the class P(p,α,β). Furthermore, we examine some properties for a class Tp(α,β) of analytic functions with negative coefficients.