Let $(E,\left \| . \right \|)$ be an ordered Banach space and $T: E\times E\rightarrow E$ an operator.

$T$ is said to bemonotone demicontinuous in (x,y), if for any two monotones sequences $(x_n)_{n\in\mathbb{N}}$ and $(y_n)_{n\in\mathbb{N}}$ in $E$ that converge strongly to $x$ and $y$ respectively, the sequence $(T(x_n,y_n)_{n\in\mathbb{N}}$ converges weakly to $T(x,y)$.

It's obvious that a continuous function is demi-continuous. I look for an example of a demi-continuous function which is not continuous.


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