Landau–Bloch type theorems for strongly bounded harmonic mappings
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In this paper, we first establish the sharp version of Landau–Bloch type theorem for strongly bounded harmonic mappings by considering the Landau–Bloch type theorem of a one-parameter family of holomorphic mappings. Next, we will establish two sharp versions of Landau–Bloch type theorems for certain harmonic mappings. Finally, we also pose several conjectures for the sharp version of Landau–Bloch type theorem for bounded harmonic mappings.
KeywordsLandau–Bloch type theorem Landau theorem Bloch theorem Planar harmonic mapping Univalent
Mathematics Subject ClassificationPrimary 30C99 Secondary 30C62