A MINIMUM THEOREM FOR THE RELATIVE ROOT NIELSEN NUMBER

In [1], a relative root Nielsen number $N_{rel}(f;\;c)$ is introduced which is a homotopy invariant lower bound for the number of roots at $c\;{\in}\;Y$ for a map of pairs of spaces $f\;:\;(X,\;A)\;{\rightarrow}\;(Y,\;B)$. In this paper, we obtain a minimum theorem for $N_{rel}(f;\;c)$ under some new assumptions on the spaces and maps which are different from those in [1].