Applications of Schwarz's Lemma to a different class

In this thesis, we will introduce a different class of analytic functions and obtain new results on this class. Utilizing the Schwarz lemma, we derive important results concerning the upper bounds of the second and third Taylor coefficients for functions within this class. The study is further enriched by applying the Julia-Wolff lemma to analyze the boundary behavior of functions in this class. These findings contribute to the broader understanding of analytic functions and their geometric properties, especially regarding their angular limits and boundary derivatives.