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december 2017 Common value pairs and their estimations
Ying Gu, Xuezhi Zhao
Bull. Belg. Math. Soc. Simon Stevin 24(4): 725-739 (december 2017). DOI: 10.36045/bbms/1515035018

Abstract

We shall give a new treatment to intersection points of two maps, named common value pairs. Given two maps $f,g\colon X\to Y$. Instead of considering intersection points on target space $Y$, we focus on the pairs in the domains $X$, the pair $(u,v)$ with $f(u)=g(v)$. The set of all these pairs is exactly the preimage of product $f\times g$ at the diagonal in $Y^2$. We shall apply the idea of Nielsen root theory into such a general case: preimage of a set. Hence, some estimation for common value pairs and therefore for intersection points are obtained.

Citation

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Ying Gu. Xuezhi Zhao. "Common value pairs and their estimations." Bull. Belg. Math. Soc. Simon Stevin 24 (4) 725 - 739, december 2017. https://doi.org/10.36045/bbms/1515035018

Information

Published: december 2017
First available in Project Euclid: 4 January 2018

zbMATH: 06848712
MathSciNet: MR3743273
Digital Object Identifier: 10.36045/bbms/1515035018

Subjects:
Primary: ‎55M20

Rights: Copyright © 2017 The Belgian Mathematical Society

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Vol.24 • No. 4 • december 2017
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