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In this paper, we show that harmonic Bloch mappings are Lipschitz continuouswith respect to the pseudo-hyperbolic metric. This result improves thecorresponding result of Theorem 1 of [P. Ghatage, J. Yan, and D. Zheng,Composition operators with closed range on the Bloch space, Proc. Amer. Math.Soc. 129 (2000), 2039-2044]. Furthermore, we prove the similar property forharmonic quasiregular Bloch-type mappings.

Lipschitz property of harmonic mappings with respect to the pseudo-hyperbolic metric