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Thus, the following proposition is obtained.
In [8], the following Proposition is obtained.
(5) In [10] the following proposition is obtained.
The following proposition is obtained: Proposition 7 Suppose r = g.
In [4], the following results and proposition are obtained.
Proof of Proposition 2.1 (1) is obtained as follows by a straightforward calculation.
It follows from Proposition 4.1 ii), Proposition 4.3, and Proposition 4.5 that the conclusion is obtained.
However, in contrast with the previously considered scenario (see Proposition 3), here optimality is obtained for finite conferencing capacity.
As observed in the previous proposition, the map (f^) is obtained as a uniform limit of the sequence (f_{n} t,z) = (varphi ^{n}_{t} z),z)), where (varphi^{n}_{t} z)) is continuous in t and holomorphic in z.
It follows from Proposition 2.1 and Proposition 2.2 that the conclusion is obtained.
By virtue of the De Giorgi iteration technique, we deduce an a priori L ∞ bound for solutions to the regularized problems in Proposition 3.2; and the uniform lower bound estimate is obtained in Proposition 3.5.
