Thus, for ( x, y ) ∈ M r 0, we have ∥ F ( x, y ) − ∥ ≤ r 0. Hence, we obtain a bounded subset M r 0 ⊆ X × Y such that T ( M r 0 ) ⊆ M r 0. In consequence, by the Schauder fixed point theorem, F has a fixed point ( x, y ) ∈ M r 0. Hence, ( x, y ) is a bounded solution of (5).
This lack of operational competence could in theory be fixed over time, but it has important short-term consequences for American grand strategy.
Having in mind the basic definition of risk, being the product of the probability and consequence, and fixing the consequence at the highest level, only probability of unfavourable event (leakage and/or failure) has been evaluated.
Extreme genome reduction has been observed in obligate intracellular insect mutualists and is an assumed consequence of fixed, long-term host isolation.
"We do, as parents, make mistakes and then we either have to live with them or suffer the consequences in fixing them.
Hence the fixed point theory in such spaces may be a consequence of the fixed point theory in certain metric spaces.
Therefore, the observed effect is obviously a consequence of fixing the torsional modes due to the spatial confinement of the chains in CP/O300 nanocomposites.
As a consequence, vesicles touching the membrane in fixed tissue may in fact have been at a short distance from the membrane.
Some consequences on existing fixed point theorems are also derived.
Some consequences on existing fixed point theorems are provided.
Events whose causes and consequences had been fixed in her mind for decades mutated in the half-light of Bob's revelations.
