For an arbitrary entire function f(z), let M(f;R) = maxjzj=R jf(z)j and m(f; r) = minjzj=r jf(z)j. If P(z) is a polynomial of degree n having no zeros in jzj < k, k 1, then for 0 r k, it is proved by Aziz et al. that M(P0; ) n +k f( +k k+r )n[1 k(k)(nja0jkja1j)n (2+k2)nja0j+2k2ja1j ( r k+ )( k+r k+ )n1]M(P; r) [ (nja0j+k2ja1j)(r+k) (2+k2)nja0j+2k2ja1j [(( +k r+k )n 1) n( r)]]m(P; k)g: In this paper, we obtain a re nement of the above inequality. Moreover, we obtain a generalization of above inequality for M(P0;R), where R k.
Zireh, A. (2011). Maximum modulus of derivatives of a polynomial. International Journal of Nonlinear Analysis and Applications, 2(2), 109-113. doi: 10.22075/ijnaa.2011.106
MLA
A. Zireh. "Maximum modulus of derivatives of a polynomial". International Journal of Nonlinear Analysis and Applications, 2, 2, 2011, 109-113. doi: 10.22075/ijnaa.2011.106
HARVARD
Zireh, A. (2011). 'Maximum modulus of derivatives of a polynomial', International Journal of Nonlinear Analysis and Applications, 2(2), pp. 109-113. doi: 10.22075/ijnaa.2011.106
VANCOUVER
Zireh, A. Maximum modulus of derivatives of a polynomial. International Journal of Nonlinear Analysis and Applications, 2011; 2(2): 109-113. doi: 10.22075/ijnaa.2011.106
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