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You would need your daily fix, or at least a fix now and then, and unless you got that you would start to feel pain," said Nummenmaa.
It's at least a fix.
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Thus, all the hypotheses of Theorem 3.2 are satisfied and T has at least a fixed point; here 0 and 2 are two fixed points of T. On the other hand, T is not a fuzzy contractive mapping of Gregori and Sapena [6].
From the Schaefer fixed-point theorem, (mathcal{A}) has at least a fixed point.
(u_{0}=u,u_{1}=v); (u_{n+1}in R u_{n}),ninmathbb{N}); the sequence ((u_{n})) is convergent and its limit is a fixed point of R. Note that each (MWPO) has at least a fixed point.
Appealing to Schauder's fixed-point theorem, F i Ψ has at least a fixed point on Λ i. □.
It follows that ∥ P z ∥ W ≤ r ˜ for all z ∈ B, and hence P B ⊂ B. An application of Schauder's fixed point theorem shows that there exists at least a fixed point z of P in W. Then y = z + ϕ ˜ is the solution to (1.9 - 1.10), and the proof is completed.
This implies that v is bounded independently of λ ∈ ( 0, 1 ), and hence by Schaefer's fixed point theorem (Theorem 4.3.2 of [22]), K c has at least a fixed point, i.e., for given c, equation (7) is solvable.
But since any territorial system is vulnerable to tax-avoidance schemes — like shifting income abroad to make it look as if profits were being earned abroad — you'd also need tough anti-abuse provisions, like taxing at least a fixed percentage of foreign earnings and limiting companies' ability to channel income to subsidiaries in low-tax countries.
Therefore, map P has at least a fixed point x 0 ∈ R n.
Thus f 2 has at least a fixed point in the interval [0,M 2].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com