The Norm Estimates of PreSchwarzian Derivatives of Spirallike Functions and Uniformly Convex α-spirallike Functions

For a constant α∈(−π/2,π/2), we define a subclass of the spirallike functions, SPp(α), the set of all functions f∈A \re{e−iαzf′(z)f(z)}≥∣∣∣zf′(z)f(z)−1∣∣∣. In the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative Tf=f′′/f′ where ∥Tf∥=supz∈Δ(1−|z|2)|Tf(z)| for the functions in SPp(α).