Applications of the jack's lemma for the holomorphic functions

In this thesis, the boundary behaviors for the different classes of holomorphic and bound functions in the unit circle are examined and Schwarz 's lemma is given for this different class. In addition, different versions of the Schwarz lemma for this class are discussed at the border. In the obtained results, the angular derivative of the function has been examined at the boundary point of the unit disc by assuming the presence of an angular limit at the boundary of the unit disk.