Homotopies for computation of fixed points on unbounded regions

Givenf: Rn→ Rn* with some conditions, our aim is to compute a fixed pointx ∈ f(x) off; hereRn isn-dimensional Euclidean space andRn* is the collection of nonempty subsets ofRn. A typical application of the algorithm can be motivated as follows: Beginning with the constant mapf0:Rn → {0} ⊂Rn and its fixed pointx0 = 0, we deformft ast → ∞ tof∞∈ f and follow the pathxt of fixed points offt. Cluster points of thext's ast → ∞ are fixed points off.