International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 91535, 8 pages
Behavior of the Trinomial Arcs when
1Forces Armées Royales Boulevard 49, Apartment no. 9, Nador 62000, Morocco
2Department of Mathematics, Faculty of Sciences, Mohamed first University, P.O. Box 524, Oujda 60000, Morocco
Received 12 April 2007; Revised 14 July 2007; Accepted 12 August 2007
Academic Editor: Teodor Bulboaca
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.
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 .