Let (H,) be a real Hilbert space and let K be a compact and connected subset of H. We show that every continuous mapping T:K \rightarrow K satisfying a mild condition has a fixed point.
"A fixed point theorem for a compact and connected set in Hilbert space,"
Turkish Journal of Mathematics: Vol. 35:
2, Article 10.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss2/10