Coincidence principles and fixed point theory for mappings in locally convex spaces (Q1293541)

The author studies coincidences for concentrative maps between locally convex spaces. Here, a continuous map \(f\) from a subset \(C\) of a locally convex vector space \(E\) with a generating system \(P\) of seminorms is said to be concentrative if \(\alpha_p(f(M))<\alpha_p(M)\) whenever \(p\in P\) and \(M\subset C\) is not precompact in the pseudometric space \((E,p)\) where \(\alpha_p\) is the ball measure of noncompactness in \((E,p)\). These results are then applied in the Banach space case to obtain fixed point theorems for maps which may be represented as a sum of two mappings, e.g., an \(m\)-accretive map and a condensing map. There is an application to the existence problem of a boundary value problem of the form \(y''+f(t,y,y')=0\), \(t\in[0,1]\), \(y(0)=y(1)=0\) where \(H\) is a real Hilbert space and \(f:[0,1]\times H\times H\to H\) is continuous and satisfies appropriate growth conditions.