đť‘šth roots of the identity operator and the geometry conjecture
Stephen Simons · 2021
In this paper, we give three different new proofs of the validity of the geometry conjecture about cycles of projections onto nonempty closed, convex subsets of a Hilbert space.The first uses a simple minimax theorem, which depends on the finite dimensional Hahn-Banach theorem.The second uses Fan's inequality, which has found many applications in optimization and mathematical economics.The third uses three results on maximally monotone operators on a Hilbert space.