Abstract: In this paper the upper bound for the derivative of 5-th degree complex polynomials norm according to a2
and p
complex polynomials norms are studied, for this kind of polynomials, the best possibilities have found. For this Brinstein Type inequalities Clement Frappier has been published a relation for complex polynomials of degree n≥6
(Theorem 8, [9]), but for n=2, 3, 4 and 5 do not exist a unique relation. I have obtained the best possibility for d5
in the following relation. Let pz≔j=15ajzjϵPn
; then p'+d5a2≤5p,
d5 is the smallest positive rot of the following equation. 80-286x2+16x3+106x4+12x5-x6=0
Keywords: Norm Preserving, Positive Defined, Hadamard Product, Hermitian Matrix, Linear Complex Spaces, Analytic Function.
Title: Improving of Bernstein type Inequality for Complex Polynomials of Degree 5 Belongs to a2
Author: Mohammad khan Haidary
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
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