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However, it appears that Yahoo was not included on this list and tech site Cnet has reported that some people were able to obtain usernames and passwords from the company before it was able to apply the fix.
"Apparently, even though they fixed the issue internally, OEMs [Original Equipment Manufacturers] did not apply the fix (perhaps they forgot or simply missed it)," Beniamini told TechCrunch in a message.
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Consequently, Theorem 4.4 allows us to apply the fixed point theorem to ℋ, which implies the existence of unique fixed point x0 ∈ B δ. This, according to Theorem 4.2, means that there exists a unique solution of (3.8).
Now thanks to Lemma 4.3 we can apply the fixed point theorem to ℱ θ, which implies the existence of unique fixed point x0 ∈ B δ. This, according to Theorem 4.2, means that there exists a unique solution of (3.8).
We apply the fixed point method to prove the stability of the systems of functional equations.
We want to apply the fixed point theorem (Theorem 2.4) to obtain the desired result.
To apply the fixed point theory, we need to define the complete metric space as follows.
We apply the fixed point theorem in a cone to obtain our result.
We rewrite (4) in two different integral forms to which we apply the fixed point method.
Many of published papers about fractional differential equations and inclusions apply the fixed point theory for proving the existence results.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com