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Exact(4)
By the definition of the function φ, we get ϵ = 0 which is contraction.
In [1] the authors gave an example of a map which is contraction for but not for the euclidian distance.
He and his colleagues do not measure recessions by the classic definition, which is contraction in inflation-adjusted gross domestic product (GDP) in consecutive quarters.
The authors there gave an example of a function which is contraction in the category of cone metric spaces but not contraction if considered over metric spaces and hence, by proving a fixed point theorem in cone metric spaces, ensured that this map must have a unique fixed point.
Similar(56)
Therefore,, which is a contraction.
that is,, which is a contraction.
This implies (|u_{1}|<|u_{1}|), which is a contraction.
Then, from (3.23), we have, which is a contraction.
By the definition of a function ψ, we get ϵ = 0 which is a contraction.
If not, since is nondecreasing and, there exists such that, then for, when as and we get, which is a contraction.
Previously, Daninos' company FACEL, which is a contraction of the company name Forges et Ateliers de Construction d'Eure et de Loire, manufactured everything from kitchen sinks and office furniture to scooters and combustion chambers for deHavilland and Rolls-Royce jet engines.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com