Iterated Function Systems composed of generalized theta-contractions

Pasupathi, Rajan ; Navascués, María Antonia (Universidad de Zaragoza) ; Chand, A.K. Bedabrata

Resumen: The theory of iterated function systems (IFSs) has been an active area of research on fractals and various types of self-similarity in nature. The basic theoretical work on IFSs has been proposed by Hutchinson. In this paper, we introduce a new generalization of Hutchinson IFS, namely generalized θ-contraction IFS, which is a finite collection of generalized θ-contraction functions T1, . . . , TN from finite Cartesian product space X × · · · × X into X, where (X, d) is a complete metric space. We prove the existence of attractor for this generalized IFS. We show that the Hutchinson operators for countable and multivalued θ-contraction IFSs are Picard. Finally, when the map θ is continuous, we show the relation between the code space and the attractor of θ-contraction IFS.

Idioma: Inglés

DOI: 10.3390/fractalfract5030069

Año: 2021

Publicado en: Fractal and fractional 5 (2021), 5030069 [14 pp.]
ISSN: 2504-3110

Factor impacto JCR: 3.577 (2021)

Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 18 / 108 = 0.167 (2021) - Q1 - T1

Factor impacto CITESCORE: 2.8 - Mathematics (Q2) - Physics and Astronomy (Q3)

Factor impacto SCIMAGO: 0.644 - Statistical and Nonlinear Physics (Q2) - Analysis (Q2)

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)