On the maximum modulus of a polynomial and its polar derivative

For a polynomial p ( z ) of degree n , having all zeros in | z | ≤ 1, Jain is shown that max | z | = 1 | D α t ⋯ D α 2 D α 1 p ( z ) | ≥ n ( n − 1 ) ⋯ ( n − t + 1 ) 2 t × [ { ( | α 1 | − 1 ) ⋯ ( | α t | − 1 ) } max | z | = 1 | p ( z ) | + { 2 t ( | α 1 | ⋯ | . For a polynomial p ( z ) of degree n , having all zeros in | z | ≤ 1, Jain is shown that max | z | = 1 | D α t ⋯ D α 2 D α 1 p ( z ) | ≥ n ( n − 1 ) ⋯ ( n − t + 1 ) 2 t × [ { ( | α 1 | − 1 ) ⋯ ( | α t | − 1 ) } max | z | = 1 | p ( z ) | + { 2 t ( | α 1 | ⋯ | .