For a polynomial
, having all its zeros in
we obtain a refinement of a known result 
(by using certain coefficients of
), and an inequality, similar to known result involving
), 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,