A φ-Contractivity Fixed Point Theory and Associated φ-Invariant Self-Similar Sets
Year: 2024
Type: article
Abstract: In this paper, we apply a generalized variant of the concept of fixed point theory due to contraction mappings on metric spaces to construct a general class of iterated function systems relative to the so-called φ-contraction mappings on a metric space. In particular, we give a general framework to the Hutchinson method of constructing self-similar sets as fixed points of suitable mappings issued from the φ-contractions on the metric space. The results may open a new axis in the generalization of self-similar sets and associated self-similar functions. Moreover, our results may be extended to general metric spaces with suitable assumptions. The theoretical results are applied for the computation of the fractal dimension of a concrete example of the new self-similar sets.
Source: Contemporary Mathematics
Author: Nifeen H. Altaweel
Institution: University of Tabuk
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403387144