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The Schwarz lemma as one of the most influential results in complex analysisand it has a great impact to the development of several research fields, suchas geometric function theory, hyperbolic geometry, complex dynamical systems,and theory of quasi-conformal mappings. In this note we mainly consider variousversion of Schwarz lemma and its relatives related to holomorphic functionsincluding several variables.

Schwarz lemma and Kobayashi metrics for holomorphic and pluriharmonic functions