On an extension of Nunokawa’s lemma

Jack’s Lemma says that if f(z) is regular in the disc $$|z|\le r$$ | z | ≤ r , $$f(0)=0$$ f ( 0 ) = 0 , and |f(z)| assumes its maximum at $$z_0$$ z 0 on the circle $$|z|=r$$ | z | = r , then $$z_0f'(z)_0/f(z_0)\ge 1$$ z 0 f ′ ( z ) 0 / f ( z 0 ) ≥ 1 . This Lemma was generalized in several directions. In this paper we consider an improvement of some first author’s results of this type.