Sentence examples for mapping principle implies from inspiring English sources

Eventually, the contraction mapping principle implies a unique fixed point of Q in B r which is the unique strong solution u ∈ Y. □.

Thus the Banach contraction mapping principle implies that (widetilde{A}^{m_{0}}) has a unique fixed point (x^) in (C(I)), and so (widetilde{A}) has a unique fixed point (x^) in (C(I)).

Thus the Banach contraction mapping principle implies that has a unique fixed point in, and so has a unique fixed point in ; by the definition of has a unique fixed point in, that is, is the unique solution of (1.1).

Therefore the Banach Contraction Mapping Principle implies that there exists a unique element such that.

(Banach contraction mapping principle [6]).

Therefore by the Banach Contraction Mapping Principle, which implies that there exists a unique element such that.

Perhaps most important, Dr. Wolfram said, his principle implies that there is no gradation between simple and sophisticated computers.

The maximum principle implies and in.

Then the comparison principle implies (3.6).

It is easily checked that this principle implies (P.5).

Then the demiclosedness principle implies that for all.