In effect, Brouwer is saying that we can assert the weak negations of the propositions expressed in these questions; hence, these propositions are so-called "Brouwerian counterexamples" or "weak counterexamples" to PEM.
Consequently, we can apply Lemma 2.5 with K = Fix ( T ) to assert the weak convergence of { x n } to a point in Fix ( T ).
In any case, those who assert a weak or intermediate global supervenience thesis while denying the corresponding strong global supervenience thesis need to provide an explanation of why weak or intermediate global supervenience holds that does not entail that strong global supervenience holds.
Clearly, then, to assert the weak negation of A is not to assign a truth value besides true and false to it; Barzin and Errera's claim (see section 4.3 below) that its treatment of negation turns Brouwer's logic into a three-valued one is groundless.
Al-Baridi's family was of Basran origin, and had served the Abbasids in various roles as officials before managing to assert a weak hold over Khuzistan.
Thus someone who asserts a weak supervenience thesis but denies the corresponding strong supervenience thesis must provide an explanation of why the weak supervenience thesis is true that does not entail that the relevant strong supervenience thesis is true as well.
One of the well-known results is proven by Reich [16] for a nonexpansive mapping T on C, which asserts the weak convergence of the sequence { x n } generated by (1.10) in a uniformly convex Banach space with a Frechet differentiable norm under the control condition ∑ n = 1 ∞ α n ( 1 − α n ) = ∞.
BEIRUT, Lebanon — Gunfire and shelling rocked Damascus, Syria, and its suburbs on Wednesday as opponents of President Bashar al-Assad reported a widening campaign by the military to sow fear and death in neighborhoods where the rebels are strong and the government is too weak to assert full control.
