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Problemy Analiza — Issues of Analysis, 2023, Volume 12(30), Issue 3, Pages 50–68
DOI: https://doi.org/10.15393/j3.art.2023.13473
(Mi pa383)
 

Strong coupled fixed points and applications to fractal generations in fuzzy metric spaces

S. Ghosh, P. Saha, S. Roy, B. S. Choudhury

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah - 711103, India
References:
Abstract: In this paper, we establish a strong coupled fixed-point result for a fuzzy contractive coupling, defined between two subsets of a fuzzy metric space. The coupling is defined by combining the concepts of coupled fuzzy contractions and cyclic mappings. It is the main instrument in the paper. Uniqueness of the strong coupled fixed-point is also shown. There is a corollary and an illustrative example. An example shows that the main theorem properly contains the strong coupled fixed-point result as a corollary. We discuss an application, where construct a special type of Iterated Function System by utilizing a family of fuzzy contractive couplings; this finally leads to the generation of a strong coupled fractal set in fuzzy metric space. A fuzzy version of the Hausdorff distance between compact sets is utilized in the above process. The method of fractal generation is illustrated.
Keywords: fuzzy metric space, iterated function system, coupling, strong coupled fixed point, strong coupled fractal.
Funding agency Grant number
University Grants Commission
Indian Institute of Engineering Science and Technology, Shibpur
The first author acknowledges UGC, India for supporting him as SRF. The third author acknowledges Indian Institute of Engineering Science and Technology, Shibpur for supporting him as SRF.
Received: 20.02.2023
Revised: 05.06.2023
Accepted: 12.06.2023
Document Type: Article
UDC: 517.98
MSC: 54H25, 47H10, 37C25
Language: English
Citation: S. Ghosh, P. Saha, S. Roy, B. S. Choudhury, “Strong coupled fixed points and applications to fractal generations in fuzzy metric spaces”, Probl. Anal. Issues Anal., 12(30):3 (2023), 50–68
Citation in format AMSBIB
\Bibitem{GhoSahRoy23}
\by S.~Ghosh, P.~Saha, S.~Roy, B.~S.~Choudhury
\paper Strong coupled fixed points and applications to fractal generations in fuzzy metric spaces
\jour Probl. Anal. Issues Anal.
\yr 2023
\vol 12(30)
\issue 3
\pages 50--68
\mathnet{http://mi.mathnet.ru/pa383}
\crossref{https://doi.org/10.15393/j3.art.2023.13473}
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