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 : 20 | Download : 8

Publication Date : 2019-06-01

Article Type : Other

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