New Quasi-Coincidence Point Polynomial Problems

Yi-Chou Chen and Hang-Chin Lai

Journal of Applied Mathematics, 2013, vol. 2013, 1-8

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:959464

DOI: 10.1155/2013/959464

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