Sentence examples for weakly but not from inspiring English sources

Güler [16] constructed a proximal point iteration that converges weakly but not strongly.

An example of the authors, Bauschke et al. [4] also showed that the proximal algorithm only converges weakly but not strongly.

This question was solved by Güler [7], who introduced an example for which the sequence { x n } generated by (1.2) converges weakly, but not strongly.

Thus for example, an action which causes an organism to leave an additional 10 offspring, but causes each organism(s) with which it interacts to leave an additional 20 offspring, is weakly but not strongly altruistic.

As the incompleteness results in particular teach us, there are sets which are only weakly but not strongly representable (the key example being the set of statements provable in the system).

Let ({v_{m}}_{m}) be a Palais-Smale sequence of (F_{mu} u)) at level (d>0), and assume that ({v_{m}}_{m}) converges weakly but not strongly to zero in (W^{1,p} (Omega )).

Thus f and g are R-weakly commuting but not R-weakly commuting of type ( A f ).

(This does not apply to (mathfrak{B }), which is weakly branch but not branch group.

Then the pair ( f, g ) is weakly commutative but not commutative.

Then f and g are weakly compatible but not conditionally sequential absorbing.

In Example 2.3, the pair ( f, g ) is weakly compatible but not conditionally sequential absorbing.