Definition:Strictly Progressing Mapping

Definition

Let $g$ be a class mapping.

Definition 1

$g$ is a strictly progressing mapping if and only if:

$\forall x \in \Dom g: x \subsetneqq \map g x$

Definition 2

$g$ is a strictly progressing mapping if and only if:

$g$ is a progressing mapping which has no fixed point.

Also see

• Equivalence of Definitions of Strictly Progressing Mappings

• Results about strictly progressing mappings can be found here.