International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2007 / Article

Research Article | Open Access

Volume 2007 |Article ID 091535 | https://doi.org/10.1155/2007/91535

Kaoutar Lamrini Uahabi, Mohammed Zaoui, "Behavior of the Trinomial Arcs B(n,k,r) when 0<α<1", International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 091535, 8 pages, 2007. https://doi.org/10.1155/2007/91535

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

Academic Editor: Teodor Bulboaca
Received12 Apr 2007
Revised14 Jul 2007
Accepted12 Aug 2007
Published30 Dec 2007

Abstract

We deal with the family B(n,k,r) of trinomial arcs defined as the set of roots of the trinomial equation zn=αzk+(1α), where z=ρeiθ 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).

References

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  2. S. Dubuc and M. Zaoui, “Sur la quasi-convexité des arcs trinomiaux,” Rendiconti del Circolo Matematico di Palermo, vol. 45, no. 3, pp. 493–514, 1996. View at: Google Scholar | Zentralblatt MATH | MathSciNet
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Copyright © 2007 Kaoutar Lamrini Uahabi and Mohammed Zaoui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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