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Then is a decreasing sequence.
Let be a decreasing sequence.
{ f k } is a decreasing sequence.
Clearly that, is a decreasing sequence.
So ({F(x_{n})}) is a decreasing sequence.
Since is a cyclic -contraction map, is a decreasing sequence.
We consider a decreasing sequence such that and.
We get that is a decreasing sequence, so (3.9).
Define now a decreasing sequence such that (4.36).
If is a decreasing sequence converging to, then (3.14).
We then get a decreasing sequence, that is, for.
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