Inequalities involving weighted means in a disc of the complex plane

For complex numbers z(j) with \ zj - 1 \ less than or equal to r, r< 1, we consider the weighted means H = (Sigma(j=1)(n)lambda(j)z(j)(-1))(-1), G = P i(j=1)(n)lambda(j)z(j). We prove, among other results, that (1-r(2))\ A \ less than or equal to \ H \ less than or equal to \ A \/1-r(2 ) and 1-r/2rln(1+r/1-r)exp(1-1-r/2rln1+r/1-r)\ G \ less than or equal to \ H \ le ss than or equal to \ G \/root 1-r(2). (C) 2000 Academic Press.