Abstract
Let w(z) = P[F](z) be a harmonic mapping defined in the unit disk D with the boundary function F satisfying w(0) = 0 and w(D) C D.In this paper by using Poisson formula and directional derivation,we prove a variant of Schwarz-Pick lemma for w(z) as follows:Λ_w(z) ≤ max h(x,r),0≤x≤1where h(x,r) is a continuous function of x which is given by(3.2).Furthermore,for some boundary functions F we prove that the above estimate is sharp.
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