Uniqueness part of the Schwarz lemma at the boundary

Abstract

In this paper, a boundary version of the uniqueness (or, rigidity) part of the Schwarz lemma should be investigated. Also, new results related to inner functions, inner capacities, and bilogaritmic concave majorants are obtained.

Uniqueness part of Schwarz lemma for driving point impedance functions

“…In recent years, a boundary version of Schwarz lemma was investigated in S.G. Krantz [10], D. Burns and S.G. Krantz [5], Dov Chelts [6], H. P. Boas [4], M. Mateljevi´c [12], Ornek-Akyel [19,20] and a few other authors' papers. They studied the uniqueness portion of the Schwarz lemma.…”

Note on the uniqueness holomorphic function on the unit disk

“…Recently similar problems were investigated in ( [6]) and ( [7]). For more detail literature and the other types of the results, we refer to ( [8]), ( [9]), ( [5]), ( [10]) and references therein.…”