There is at most one continuous invariant mean

Abstract

We show that, for a (not necessarily continuous) weakly contractive mean-type mapping $\mathbf{M}:I^p\to I^p$ (where $I$ is an interval and $p\in \mathbb{N}$), the functional equation $K\circ \mathbf{M}=K$ has at most one solution in the family of continuous means $K:I^p\to I$. Some general approach to the latter equation is also given.

References in corpus (1)

• Mean-type mappings and invariance principle

Cited by in corpus (1)

• Invariance property for extended means