The averaging theorem of lefschetz coincidence numbers and estimation of nielsen coincidence numbers

Throughout this paper, we will work in the category of compact connected manifolds and continuous maps. If $X_1, X_2$ are manifolds, $f, g: X_1 \to X_2$ are maps, then a point $x \in X_1$ is a coincidence of f and g iff f(x) = g(x) ; the set of all such points is denoted by Coin(f,g).