We find conditions on the complex-valued functions A, B, C, D defined in the unit disc U and the positive constants M and N such that vertical bar A(z) zp' (z) + B(z) p(2) (z) + C(z) p(z) + D(z)vertical bar < M implies vertical bar p(z)vertical bar < N, where p is analytic in U, with p(0) = 0.
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