• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.245-252
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• 1996

The relative Nielsen number N(f;X,A) was introduced in 1986. It gives us a better, and ideally sharp, lower bound for the minimum number MF[f;X,A] of fixed points in the homotopy class of the map $f;(X,A) \to (X,A)$. Similarly, we also can think about the Nielsen map $f:(X,A) \to (X,A)$. Similarly, we also can be think about the Nielsen root theory. In this paper, we introduce a relative root Nielsen number N(f;X,A,c) of $f:(X,A) \to (Y,B)$ and show some basic properties.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.701-707
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• 1997

In [8], we introduce the relative root Nielsen number N(f;X, A, c) for maps of pairs of spaces $f : (X, A) \to (Y, B)$. From it, we obtain some immediate consequences of the definition and illustrate it by some examples. We consider the question whether there exists a map $g : (X, A) \to (Y, B)$ homotopic to a given map $f : (X, A) \to (Y, B)$ which has precisely N(f;X, A, c) roots, that is, the minimum theorem for N(f;X, A, c).