ABSTRACT
Finding fixed points is closely related to solving equations. Indeed, x is a solution of f(x) = y if and only if x is a fixed point of the mapping F (x) = f(x) + x− y. Let us consider an equation of the type f(x) = y, where y is a given point in the plane, and f is a continuous mapping of a disk D into the plane, which distorts the disk in some complicated way. We are interested in conditions on the behavior of f restricted to the boundary of D that guarantee that f(D) contains y. For this purpose, we define the ‘winding number’ which counts how many times f wraps the boundary of D around y.
