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Exact(41)

Therefore, Θ m is closed.

Since ran M is closed, so is ran M* (by, e.g., [[1], Corollary 15.34]).

Assume that C m is closed and convex for some positive integer m.

Moreover, they are complete if and only if M is closed.

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Similar(19)

Let C m be closed and convex for some m ∈ N.

Let ( X, d ) be a metric space, m ∈ N, A 1, A 2, …, A m be closed nonempty subsets of X and X = ⋃ i = 1 m A i.

Let C 1,...,C m be closed convex subsets of the Hilbert space (mathcal {H}), whose intersection (C=cap _{i=1}^{m}C_{i}) is non-empty.

Let ( X, d ) be a complete metric space, m be a positive integer, A 1, …, A m be closed nonempty subsets of X, Y : = ⋃ i = 1 m A i and f : Y → Y be an operator.

Let ( X, d ) be a complete metric space, m ∈ N, A 1, A 2, …, A m be closed nonempty subsets of X and X = ⋃ i = 1 m A i. Suppose that f is a cyclic weaker φ-contraction.

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