Question: Let F be a nonempty, closed and bounded, convex subset of C(X), the space of continuous functionals on a compact metric space X. Let T:

Let F be a nonempty, closed and bounded, convex subset of C(X), the space of continuous functionals on a compact metric space X. Let T: F → F be a continuous operator on F. If the family T(F) is equicontinuous, then T has a fixed point.

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