Abstract
Our purpose in this paper is to consider a new class of iterated
function systems (IFS) based on the concept of orbital condition
introduced by R. Miculescu et al. (Iterated function systems consisting
of continuous functions satisfying Banach’s orbital condition, Analele
Universităt¸ii de Vest, Timi¸soara, Seria Matematică-Informatică LVI, 2,
(2018),71-80). On the given IFS there are imposed some sufficient
conditions guaranteeing the existence of an attractor. There are also
established some further results which describe the nature of the
attractors of the considered type. The introduced theory is supported by
some examples of IFSs for which the attractors are also depicted.