Abstract
It is shown that the set of fixed points of a non-expansive operator is either empty or closed and convex. Under rather general conditions this shows that the minimum norm solution of an operator equation of the form x = Tx exists and is unique, provided that T is non-expansive. This holds in any strictly convex Banach space, a class of spaces that includes Hilbert spaces as particular case, and has consequences in signal and image reconstruction, as well as in other engineering applications.
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