  We investigate the existence of subinvariant metric functionals for commuting
families of nonexpansive mappings in noncompact subsets of Banach spaces. Our
findings underscore the practicality of metric functionals when searching for
fixed points of nonexpansive mappings. To demonstrate this, we additionally
investigate subsets of Banach spaces that have only nontrivial metric
functionals. We particularly show that in certain cases every metric functional
has a unique minimizer; thus, subinvariance implies the existence of a fixed
point.
