Therefore, by Lemma 2.1, provided that condition (3.4) is satisfied, the order-1 periodic solution ((phi(t), psi(t))) of system (1.2) is orbitally asymptotically stable.
If the information provided by Microsoft does not satisfy the order, the company will face a fine of 3 million euros a day, backdated to July, Mr. Todd said.
Then there exists a point x ∈ X such that x α ⊂ F x provided that X satisfies the order sequential limit property.
Then C α ( F, g ) ≠ ϕ provided that X satisfies the order sequential limit property and ( F ( X ) ) α ⊆ g ( X ) for each α.
In our setting, a single buyer decides on the order quantity to fill end-customer demand and a single supplier produces to satisfy the order from the buyer as described in the beginning.
An ordered metric space is said to satisfy the order sequential limit property if ( u n, z ) ∈ ∇ for all n, whenever a sequence u n → z and ( u n, u n + 1 ) ∈ ∇ for all n.
Next, we will show that, under the same hypothesis, the orbit O = G ⋅ 0 must satisfy the order 3 condition.
Proposition 3.5 If the orbit O of G through 0 ∈ b M verifies T 0 (O ) ⊂ T 0 c (b M ), then it satisfies the order 3 condition.
If the orbit O of G through 0 ∈ b M verifies T 0 (O ) ⊂ T 0 c (b M ), then it satisfies the order 3 condition.
"The two of us, working our 15 to 20 hours a week, barely produce enough to satisfy the orders coming in," Ms. Barrack said.
