Weak subordination for convex univalent harmonic functions

For two complex-valued harmonic functions f and F defined in the open unit disk Δ with f(0)=F(0)=0, we say f is weakly subordinate to F if f(Δ)⊂F(Δ). Furthermore, if we let E be a possibly infinite interval, a function with f(⋅,t) harmonic in Δ and f(0,t)=0 for each t∈E is said to be a weak subordination chain if f(Δ,t₁)⊂f(Δ,t₂) whenever t₁,t₂∈E and t₁<t₂. In this paper, we construct a weak subordination chain of convex univalent harmonic functions using a harmonic de la Vallée Poussin mean and a modified form of Pommerenke's criterion for a subordination chain of analytic functions.