Radius of starlikeness of p-valent λ-fractional operator

摘要

Let consider Ap denoting a class of analytical functions defined as f(z)=zp+ap+1zp+1+⋯+ap+nzp+n+⋯ and p-valent in unit disc U={z||z|<1}. f(z) ∈ Ap is expressed to be p-valently starlike in U if there is a positive figure ρ fulfilling ρ < |z| < 1, Re(zf′(z)f(z))>0, and ∫02πRe(zf′(z)f(z))dθ=2pπ, z=reiθ, ρ < r < 1. Let us consider S*(p) denoting the family of f(z) in Ap, 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).