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Open AccessArticle

Multi Fractals of Generalized Multivalued Iterated Function Systems in b-Metric Spaces with Applications

by Sudesh Kumari 1,†, Renu Chugh 2,†, Jinde Cao 3,*,† and Chuangxia Huang 4,*,†
1
Department of Mathematics, Government College for Girls Sector 14, Gurugram 122001, India
2
Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, India
3
Research Center for Complex Systems and Network Sciences, School of Mathematics, Southeast University, Nanjing 210096, China
4
School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, China
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(10), 967; https://doi.org/10.3390/math7100967
Received: 8 September 2019 / Revised: 4 October 2019 / Accepted: 9 October 2019 / Published: 14 October 2019
(This article belongs to the Special Issue Impulsive Control Systems and Complexity)
In this paper, we obtain multifractals (attractors) in the framework of Hausdorff b-metric spaces. Fractals and multifractals are defined to be the fixed points of associated fractal operators, which are known as attractors in the literature of fractals. We extend the results obtained by Chifu et al. (2014) and N.A. Secelean (2015) and generalize the results of Nazir et al. (2016) by using the assumptions imposed by Dung et al. (2017) to the case of ciric type generalized multi-iterated function system (CGMIFS) composed of ciric type generalized multivalued G-contractions defined on multifractal space C ( U ) in the framework of a Hausdorff b-metric space, where U = U 1 × U 2 × × U N , N being a finite natural number. As an application of our study, we derive collage theorem which can be used to construct general fractals and to solve inverse problem in Hausdorff b-metric spaces which are more general spaces than Hausdorff metric spaces. View Full-Text
Keywords: generalized multivalued G—Contraction; generalized multivalued iterated function systems; Hausdorff b metric space; fractal space; multifractal space; fixed point generalized multivalued G—Contraction; generalized multivalued iterated function systems; Hausdorff b metric space; fractal space; multifractal space; fixed point
MDPI and ACS Style

Kumari, S.; Chugh, R.; Cao, J.; Huang, C. Multi Fractals of Generalized Multivalued Iterated Function Systems in b-Metric Spaces with Applications. Mathematics 2019, 7, 967.

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