Radius of starlikeness of p-valent λ-fractional operator

Let consider A _p denoting a class of analytical functions defined as f(z)=z ^p +a _p+1 z ^p+1 +⋯+a _p+n z ^p+n +⋯ and p-valent in unit disc U={z||z|<1}. f(z)∈ A _p is expressed to be p-valently starlike in U if there is a positive figure ρ fulfilling ρ < |z| < 1, Re(z [Formula presented])>0, and ∫02πRe(z [Formula presented])dθ=2pπ, z=re ^iθ , ρ < r < 1. Let us consider S*(p)denoting the family of f(z)in A _p , being regular and p-valently starlike in U. It was proved by Goodman [3]that f(z)∈ S*(p)is at most p-valent in U. In present study, some results about radius of starlikeness of p-valent λ-fractional operator were obtained. Also some relevant corollaries were given. Finally, a result associated with p-valent λ-fractional operator by using convolution was given as a conclusion. The aim of this study is to give some results on λ-fractional operator of f(z)∈ S*(p).