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Then is a decreasing sequence.
{ f k } is a decreasing sequence.
Clearly that, is a decreasing sequence.
So ({F(x_{n})}) is a decreasing sequence.
If is a decreasing sequence converging to, then (3.14).
Since is a cyclic -contraction map, is a decreasing sequence.
We get that is a decreasing sequence, so (3.9).
Thus, is a decreasing sequence, and we have that exists.
Hence is a decreasing sequence and therefore exists.
which shows that { ∥ x n − p ∥ } is a decreasing sequence of non-negative reals.
It follows that ((x_{n})_{ngeq n_{0}}) is a decreasing sequence in ((X,leq)).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com