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Let P(z)be a polynomial of degree n having all its zeros in|z|≤k,k≤1,then for every real or complex numberβ,with|β|≤1 and R≤1,it was shown by A.Zireh et al.[7]that for|z|=1,min|z|=1|P(Rz)+β(R+k/1+k)^n P(z)|≥k^-n|Rn+b(R+k/1+k)^n|min|z|=k|P(z)|.In this pape