# New Quasi-Coincidence Point Polynomial Problems

Journal of Applied MathematicsVolume 2013 2013, Article ID 959464, 8 pages

Research Article

Department of General Education, National Army Academy, Taoyuan 320, Taiwan

Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan

Received 30 April 2013; Accepted 10 July 2013

Copyright © 2013 Yi-Chou Chen and Hang-Chin Lai. 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.

Abstract

Let be a real-valued polynomial function of the form , where the degree of in is greater than or equal to . For arbitrary polynomial function , , we will find a polynomial solution to satisfy the following equation: : , where is a constant depending on the solution , namely, a quasi-coincidence point solution of , and is called a quasi-coincidence value. In this paper, we prove that i the leading coefficient must be a factor of , and ii each solution of is of the form , where is arbitrary and is also a factor of , for some constant , provided the equation has infinitely many quasi-coincidence point solutions.

Author: Yi-Chou Chen and Hang-Chin Lai

Source: https://www.hindawi.com/