Landau's theorem and marden constant for harmonic v-bloch mappings

Our main aim is to investigate the properties of harmonic v-Bloch mappings. Firstly, we establish coefficient estimates and a Landau theorem for harmonic v-Bloch mappings, which are generalizations of the corresponding results in Bonk et al. ['Distortion theorems for Bloch functions', Pacific. J. Math. 179 (1997), 241 - 262] and Chen et al. ['Bloch constants for planar harmonic mappings', Proc. Amer. Math. Soc. 128 (2000), 3231 - 3240]. Secondly, we obtain an improved Landau theorem for bounded harmonic mappings. Finally, we obtain a Marden constant for harmonic mappings. © Australian Mathematical Publishing Association Inc. 2011.