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Suppose $X$ is a reflexive Banach space with its dual to be $X'$. Let $$ x_n\rightharpoonup x~ ~in~ X. $$

Below, are two related questions:

Q1: Let $f: X\to \mathbb{R}$ be a strictly convex function and the subdifferential $\partial f: X\to X'$ exists and is unique at every point $x\in X$. Do we have $$ \partial f(x_n)\rightharpoonup \partial f(x)? $$ If not, what conditions should we put to ensure this?

Q2: Let $G: X\to X'$ an m-accretive single-valued operator (may be nonlinear) in the sense that $$ \langle G(x)-G(y), x-y\rangle >0, \forall x\neq y. $$ Do we have $$ G(x_n)\rightharpoonup G(x)? $$ If not, what conditions should we put to ensure this?

I am not very familiar with monotone operator theory. If anybody can point out a good reference that may be helpful for solving one of these two questions, I would appreciate it.

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I finally found in the paper 'Existence of weak solutions to doubly degenerate diffusion equations' written by Ales Matas et al (http://link.springer.com/article/10.1007/s10492-012-0004-0) there is a useful lemma (Lemma B.3.).

It says that essentially we need an extra condition: $$ \limsup_{n\to\infty}\langle x_n, G(x_n)\rangle \le \langle x, G(x)\rangle. $$ This answers my questions partially.