We revisit the fixed point problem for the sum of a compact operator and a continuous function, where the domain on which these maps are defined is not necessarily convex, the former map is allowed to be multi-valued, and the latter to be a semicontraction and/or a suitable nonexpansive map. In this setup, guaranteeing the existence of fixed points is impossible, but two types of invariant-like sets are found to exist.
- Fixed sets
- Krasnoselskiǐ fixed point theorem
- Nonexpansive maps
ASJC Scopus subject areas
- Applied Mathematics