Cilt:71 Sayı:03 (2022)

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On the maximum modulus of a complex polynomial
(Ankara Üniversitesi, 2022) Malik, Shabir; Other; Other
In this paper we impose distinct restrictions on the moduli of the zeros of p ( z ) = n ∑ v = 0 a v z v and investigate the dependence of ∥ p ( R z ) − p ( σ z ) ∥ , R > σ ≥ 1 on M α and M α + π , where M α = max 1 ≤ k ≤ n | p ( e i ( α + 2 k π ) / n ) | and on certain coefficients of p ( z ) . This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases. Moreover, the problem of estimating p ( 1 − w n ) , 0 < w ≤ given p ( 1 ) = 0 is considered.