Contraction Mapping Theorem:
For any metric space V that is complete (i.e. closed) under an operator T(v), where T is a γ-contraction, T converges to a unique fixed point and at a linear convergence rate of γ.
This is from field of artificial intelligence, called reinforcement learning, but I'm confused by some pure math terminology.
I know that metric space being complete means that any Cauchy sequence converges, but what means that it's complete under operator?
I read this on contraction in operator theory, is this correct interpretation of γ-contraction?