In this thesis, we will say something about the behavior of holomorphic mappings defined on the closed unit disk. We will dedicate special attention to the values of the derivatives of holomorphic mappings at the boundary fixed points that lie on the boundary of the unit disk. For estimating their values we will refer to the generalization of the Schwarz Lemma, such as Julia's inequality. In so far as we introduce additional assumptions we can even more accurately estimate the values of the derivatives at fixed boundary points of holomorphic mappings, which is well illustrated by the Anti-calculus proposition for holomorphic functions and Wolff’s proposition.
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