Behavior of the Trinomial Arcs B ( n, k, r ) when 0 < α < 1

Kaoutar Lamrini Uahabi and Mohammed Zaoui

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-8

Abstract:

We deal with the family B ( n , k , r ) of trinomial arcs defined as the set of roots of the trinomial equation z n = α z k + ( 1 − α ) , where z = ρ e i θ is a complex number, n and k are two integers such that 0 < k < n , and α is a real number between 0 and 1 . These arcs B ( n , k , r ) are continuous arcs inside the unit disk, expressed in polar coordinates ( ρ , θ ) . The question is to prove that ρ ( θ ) is a decreasing function, for each trinomial arc B ( n , k , r ) .

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:091535

DOI: 10.1155/2007/91535

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