Locally inner automorphism

Definition with symbols
An automorphism $$\sigma$$ of a group $$G$$ is termed a locally inner automorphism if, for any elements $$x_1,x_2,\dots,x_n \in G$$, there exists $$g \in G$$ such that $$gx_ig^{-1} = \sigma(x_i)$$ for $$1 \le i \le n$$.