in- NIELSEN COINCIDENCE POINT THEORY

Let f,g:X=X be maps of a compact connected Riemannian manifold, with or without boundary. For in 0 sufficiently small, we introduce an in – Nielsen coincidence number that is a lower bound for the number n^in(f,g) of coincidence points of all self – maps that are in - homotopic to f and g. We prove that there is always maps f1,g1:x rightarrow x that is in – homotopic to f and g such that f1 and g1have exactly n in-(f,g) coincidence points