# Generalized equation

This has the form: 0 is in $LaTeX: \{f(x)\} + T(x)$, where $LaTeX: f$ is a function from $LaTeX: \mathbb{R}^n$ into $LaTeX: \mathbb{R}^n$ and $LaTeX: T$ is a point to set map that maps $LaTeX: x$ into subsets of $LaTeX: \mathbb{R}^n$. If $LaTeX: T$ is absent, the condition reduces to an ordinary equation, $LaTeX: f(x)=0$. Usually, $LaTeX: T$ is assumed to satisfy the monotonicity condition:
$LaTeX: (x-x')^T(y-y') \ge 0 \mbox{ for } y \in T(x) \mbox{ and } y' \in T(x').$