Schauder's Theorem predicts the existence of a fixed point for a compact operator over a bounded, closed, convex, non-empty subset of this type of space.
Schauder's Theorem predicts the existence of a fixed point for a compact operator over a bounded, closed, convex, non-empty subset of this type of space. By definition, this construct is closed under vector addition and scalar multiplication, and every Cauchy sequence in it is convergent. One example of this topology is the Hilbert space on which an inner product gives its norm. FTP, name this complete normed vector space central to functional analysis and named for a Polish mathematician.
Schauder's Theorem predicts the existence of a fixed point for a compact operator over a bounded, closed, convex, non-empty subset of this type of space.
{Banach} Space