Journal of Prime Research in Mathematics

# Limit sets of weakly contracting relations with eventual condensation

Vasile Glavan
Moldova State University, 60 A.Mateevici St., Chisinau, Republic of Moldova; University of Podlasie, Ul. Konarskiego 2, Siedlce, Poland.
Valeriu Gutu
Moldova State University, 60 A.Mateevici St., Chisinau, Republic of Moldova.

$$^{1}$$Corresponding Author: vglavan@ap.siedlce.pl

### Abstract

Barnsley’s formula for the attractor of a hyperbolic IFS with condensation is generalized for the omega-limit set of a weakly contracting set-valued map with eventual condensation. The latter need not be a contraction, as well as its omega-limit set need not be an attractor.

#### Keywords:

Set-valued map, weak contraction, eventual condensation, attractor, limit relation, limit set, fractal.