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Again by taking 0 < β i, j < 1 and 0 ≤ γ i, j < 1, it is easy to check inequality (4) holds, thus all the hypotheses of Theorem 2.1 are satisfied and ( 0, 0, 0 ), ( 1, 1, 1 ) are the tripled coincident points of g and T i.
Similar(59)
from the proof of Theorem 6.7, we need to check inequalities (55) and (57).
In other words, if x and y are not ⪯-mixed comparable, we do not need to check inequalities (9) and (10).
In other words, if x and y are not ≼ I -comparable, we do not need to check inequalities (51) and (52).
In what follows, we check the inequality (3).
We only have to check the inequality (1.6).
Indeed it is easy to check the inequality (3.23).
It is easy to check that inequality (11) is correct for k = 1, 2 and 3.
Now we have to check the inequality of Theorem 2.1 for the following cases.
Finally, we check that inequality (57) is satisfied for ξ = 1.
It is easy to check that inequality (27) holds for every boundary point of G m, too.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com