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In this paper, we investigate the properties of locally univalent andmultivalent planar harmonic mappings. First, we discuss the coefficientestimates and Landau's Theorem for some classes of locally univalent harmonicmappings, and then we study some Lipschitz-type spaces for locally univalentand multivalent harmonic mappings.

Coefficient estimates, Landau's theorem and Lipschitz-type spaces on planar harmonic mappings