For a polynomial of degree , having all its zeros in
,
we obtain a refinement of a known result [2]

(by using certain coefficients of ), and an inequality, similar to known result involving
derivative, (
), instead of the first derivative of (and better than the
similar inequality, obtained by repeated applications of known result, in many cases).

Key Words: polynomial, derivatives, zeros in , certain coefficients, generalization of Schwarz's lemma.

2010 Mathematics Subject Classification: Primary 30C10,

Secondary 30A10.