ANALYSIS ON FRACTALS IN FUZZY METRIC SPACES

Fractals ◽  
2011 ◽  
Vol 19 (03) ◽  
pp. 379-386 ◽  
Author(s):  
D. EASWARAMOORTHY ◽  
R. UTHAYAKUMAR
Keyword(s):  
Metric Spaces ◽  
Iterated Function System ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Analysis On Fractals ◽  
Contraction Theorem ◽  
Iterated Function ◽  
Banach Contraction ◽  
Banach Contraction Theorem ◽  
Collage Theorem

In this paper, we investigate the fractals generated by the iterated function system of fuzzy contractions in the fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard fuzzy metric spaces by using the fuzzy Banach contraction theorem. In addition to that, we discuss some results on fuzzy fractals such as Collage Theorem and Falling Leaves Theorem in the standard fuzzy metric spaces with respect to the standard Hausdorff fuzzy metrics.

scholarly journals On Some Fixed Point Results in E − Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Rachid Mecheraoui ◽  
Zoran D. Mitrović ◽  
Vahid Parvaneh ◽  
Hassen Aydi ◽  
Naeem Saleem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Additional Condition ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
New Class ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Banach Contraction Theorem

In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional condition. We demonstrate the wide validity of the new class.

scholarly journals Suzuki-Type of Common Fixed Point Theorems in S-Fuzzy Metric Spaces

2021 ◽  
Vol 2 (3) ◽  
pp. 86-91
Author(s):  
M. Jeyaraman ◽  
S. Sowndrarajan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Banach Contraction ◽  
New Type ◽  
Common Fixed Point Theorems

In this paper, by using of Suzuki-type approach [Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136, 1861–1869, 2008.] we prove new type of Suzuki- type fixed point theorem for non-Archimedean S - fuzzy metric spaces which is generalization of Suzuki-Type fixed point results in S - metric spaces.

Iterated function systems and attractors in the KM fuzzy metric spaces

2015 ◽  
Vol 267 ◽  
pp. 100-116 ◽  
Author(s):  
Jian-Zhong Xiao ◽  
Xing-Hua Zhu ◽  
Pan-Pan Jin
Keyword(s):  
Metric Spaces ◽  
Iterated Function Systems ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Iterated Function

scholarly journals Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 273 ◽  
Author(s):  
Salvador Romaguera ◽  
Pedro Tirado
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Classical Theorem ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Banach Contraction

With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see “Am. Math. Month. 1967, 74, 436–437”) that a metric space is complete if and only if any Banach contraction on any of its closed subsets has a fixed point. We apply our main result to deduce that a well-known fixed point theorem due to D. Mihet (see “Fixed Point Theory 2005, 6, 71–78”) also allows us to characterize the fuzzy metric completeness.

scholarly journals A Perov Version of Fuzzy Metric Spaces and Common Fixed Points for Compatible Mappings

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1290
Author(s):  
Juan Martínez-Moreno ◽  
Dhananjay Gopal
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Compatible Mappings ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Banach Contraction

In this paper, we define and study the Perov fuzzy metric space and the topology induced by this space. We prove Banach contraction theorems. Moreover, we devised new results for Kramosil and Michálek fuzzy metric spaces. In the process, some results about multidimensional common fixed points as coupled/tripled common fixed point results are derived from our main results.

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

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 967 ◽  
Author(s):  
Sudesh Kumari ◽  
Renu Chugh ◽  
Jinde Cao ◽  
Chuangxia Huang
Keyword(s):  
Inverse Problem ◽  
Fixed Points ◽  
Natural Number ◽  
Metric Space ◽  
Metric Spaces ◽  
Iterated Function System ◽  
Hausdorff Metric ◽  
Iterated Function Systems ◽  
Iterated Function ◽  
Collage Theorem

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.

scholarly journals On Banach contraction principles in fuzzy metric spaces

2018 ◽  
Vol 19 (1) ◽  
pp. 235-248 ◽  
Author(s):  
Valentín Gregori ◽  
◽  
Juan-José Miñana ◽  
Almanzor Sapena ◽  
◽  
...  
Keyword(s):  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Banach Contraction
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