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

Abstract EN

For a normalized analytic function f defined on the unit disc ?, let ϕ(f,f′,f′′;z) be a function of positive real part in ?, ψ(f,f′,f′′;z) need not have that property in ?, and χ=ϕ+ψ.

For certain choices of ϕ and ψ, a sharp radius constant ρ is determined, 0<ρ<1, so that χ(ρz)/ρ maps ? onto a specified region in the right half-plane.