Abstract

Let Mn be the classes of regular functions f(z)=z1+a0+a1z+ defined in the annulus 0<|z|<1 and satisfying ReIn+1f(z)In+1f(z)>0, (n0), where I0f(z)=f(z), If(z)=(z1z(z1)2)f(z), Inf(z)=I(In1f(z)), and is the Hadamard convolution. We denote by Γn=MnΓ, where Γ denotes the class of functions of the form f(z)=z1+k=1|ak|zk. We obtained that relates the modulus of the coefficients to starlikeness for the classes Mn and Γn, and coefficient inequalities for the classes Γn.