Some remarks for a certain class of holomorphic functions at the boundary of the unit disc

Özet

We consider a boundary version of the Schwarz Lemma on a certain class which is denoted by 𝒦(𝛼). For the function 𝑓(𝜆) = 𝜆 + 𝑐􀬶𝜆􀬶 + 𝑐􀬷𝜆􀬷+. .. which is defined in the unit disc 𝐸 such that the function 𝑓(𝜆) belongs to the class 𝒦(𝛼), we estimate from below the modulus of the angular derivative of the function 􀰒􀯙'(􀰒) 􀯙(􀰒) at the boundary point 𝑏 with 􀯕􀯙'(􀯕) 􀯙(􀯕) = 􀬵 􀬵􀬾􀰈 . Moreover, we get the Schwarz Lemma for the class 𝒦(𝛼). We also investigate some inequalities obtained in terms of sharpness.