New aspects concerning IFSs consisting of continuous functions satisfying Banach’s orbital condition

A characterization of the fuzzy fractals generated by an orbital fuzzy iterated function system

“…Indeed, on the one hand, as u x ∈ F * X is normal for every x ∈ [u] * , we deduce that w u is normal. On the other hand, since suppu x Remark 2.8 ⊆ A x Proposition 5 from [14] ⊆…”

“…Another natural generalization of Hutchinson' concept of iterated function system, termed as orbital iterated function system, was recently considered in [9], [10] and [14]. Here the idea is to consider iterated function systems consisting of continuous functions satisfying Banach's orbital condition.…”

"A characterization of fuzzy fractals generated by an orbital fuzzy iterated function system"

“…Another natural generalization of Hutchinson's concept of iterated function system, termed as orbital iterated function system, was recently considered in [9], [10] and [14].…”

“…It comes to the light that this is a genuine generalization since there exist such systems for which the fractal operator is weakly Picard, but not Picard (see Remark 4.1 from [9]). For extra properties of this kind of system see [10] and [14].…”

Phi-contractive parent-child infinite IFSs and orbital phi-contractive infinite IFSs

“…Along these lines of research let us mention some papers. For example, in [10] L. Ioana and A. Mihail introduced and studied IFSs consisting of ϕ-contractions and in [19] I. Savu studied IFSs consisting of continuous functions satisfying Banach's orbital condition. In [6] F. Georgescu generalized the concept of IFS consisting of convex contractions and in [21] N. A. Secelean introduced a new type of IFS, namely IFS consisting of F -contractions.…”