Suppose $X$ is a real Reflexive Banach space and $f:X\rightarrow X^\star$ a pseudo-monotone map (see here for a definition of pseudo-monotone). Is there a geoemetric interpretation for this definition.
For example, we know that a differentiable $f: X: \rightarrow\mathbb{R}$ is convex if and only if $f':X\rightarrow X^\star$ is monotone. From this post we know that with the additional condition of boundedness $f$ is WSLSC. Can we deduce more about the geometry of $f$?
I know that the first one to define the notion of pseudo-monotonicity was Brezis. Does anyone know the paper there he first defined it?