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

Authors : Bülent Nafi ÖRNEK, Tuğba AKYEL

Pages : 446-452

Doi:10.16984/saufenbilder.464294

View : 23 | Download : 16

Publication Date : 2019-06-01

Article Type : Research Paper

Abstract :We consider a boundary version of the Schwarz Lemma on a certain class which is denoted by Kinsert ignore into journalissuearticles values(alfa); . For the function  finsert ignore into journalissuearticles values(z);=z+c 2 z 2 +.......  which is defined in the unit disc E such that the function f insert ignore into journalissuearticles values(z); belongs to the class Kinsert ignore into journalissuearticles values(alfa); , we estimate from below the modulus of the angular derivative of the function insert ignore into journalissuearticles values( ); insert ignore into journalissuearticles values( ); zf ` z f z at the boundary point b with insert ignore into journalissuearticles values( ); = 1 insert ignore into journalissuearticles values( ); 1 bf ` b f b  . Moreover, we get the Schwarz Lemma for the class Kinsert ignore into journalissuearticles values(alfa); . We also investigate some inequalities obtained in terms of sharpness.
Keywords : Schwarz Lemma, Holomorphic function, Jacks Lemma, Angular derivative