On the Largest Disc Mapped by Sum of Convex and Starlike Functions

Abstract

For a normalized analytic functionfdefined on the unit disc𝔻, letϕ(f,f′,f′′;z)be a function of positive real part in𝔻,ψ(f,f′,f′′;z)need not have that property in𝔻, andχ=ϕ+ψ. For certain choices ofϕandψ, a sharp radius constantρis determined,0<ρ<1, so thatχ(ρz)/ρmaps𝔻onto a specified region in the right half-plane.