Suppose w is a sense-preserving harmonic mapping of the unit disk D such that w(D) ⊆ D and w has a zero of order p ≥ 1 at z = 0. In this paper, we first improve the Schwarz lemma for w, and then, we establish its boundary Schwarz lemma. Moreover, by using the automorphism of D, we further generalize this result.
MSC Codes 30C15(Primary), 31A20, 30C62(Secondary)
|Journal||Bulletin of the Malaysian Mathematical Sciences Society|
|State||Published - 24 Jul 2020|
- Boundary Schwarz lemma
- Harmonic mappings
- Multiplicity of zeros
- Schwarz lemma