Research Article | Open Access
Kaoutar Lamrini Uahabi, Mohammed Zaoui, "Behavior of the Trinomial Arcs when ", 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 when
We deal with the family of trinomial arcs defined as the set of roots of the trinomial equation , where is a complex number, and are two integers such that , and is a real number between and . These arcs are continuous arcs inside the unit disk, expressed in polar coordinates . The question is to prove that is a decreasing function, for each trinomial arc .
- H. Fell, “The geometry of zeros of trinomial equations,” Rendiconti del Circolo Matematico di Palermo, vol. 29, no. 2, pp. 303–336, 1980.
- 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.
- S. Dubuc and A. Malik, “Convex hull of powers of a complex number, trinomial equations and the Farey sequence,” Numerical Algorithms, vol. 2, no. 1, pp. 1–32, 1992.
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