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Abstract and Applied Analysis
Volume 2013, Article ID 307913, 9 pages
http://dx.doi.org/10.1155/2013/307913
Research Article

Infinitely Many Quasi-Coincidence Point Solutions of Multivariate Polynomial Problems

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

Received 9 November 2013; Accepted 5 December 2013

Academic Editor: Wei-Shih Du

Copyright © 2013 Yi-Chou Chen. 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 . 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 of ( ). In this paper, we prove that the number of all solutions in ( ) does not exceed provided those solutions are of finitely many exist, if all solutions are of infinitely many exist, then any solution is represented as the form where is arbitrary and is also a factor of , provided the equation ( ) has infinitely many quasi-coincidence (point) solutions.