2018/03/19 by Radu Miculescu, Miculescu, Radu, Silviu Aurelian Urziceanu +1
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Lipid metabolism and disorders #Mathematical Dynamics and Fractals #Primary 28A80 #Secondary 54H20
paper · pdf · doi:10.48550/arxiv.1803.06933
openalex publication_date 2018/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, influenced by the ideas from A. Mihail, The canonical projection between the shift space of an IIFS and its attractor as a fixed point, Fixed Point Theory Appl., 2015, Paper No. 75, 15 p., we associate to every generalized iterated function system F (of order m) an operator H defined on Cm and taking values on C, where C stands for the space of continuous functions from the shift space on the metric space corresponding to the system. We provide sufficient conditions (on the constitutive functions of F) for the operator H to be continuous, contraction, phi-contraction, Meir-Keeler or contractive. We also give sufficient condition under which H has a unique fixed point. Moreover, we prove that, under these circumstances, the closer of the imagine of the fixed point is the attractor of F and that the fixed point is the canonical projection associated to F. In this way we give a partial answer to the open problem raised on the last paragraph of the above mentioned Mihail's paper.