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Feb 21, 2011 at 0:10 comment added user6976 My guess is "yes" if the contraction constant is small enough comparing to $C$. But I am not sure because I never thought about it.
Feb 21, 2011 at 0:05 comment added John H Can the Banach fixed point theorem can be used in this spaces?
Feb 20, 2011 at 23:58 history answered user6976 CC BY-SA 2.5