Expansivity and shadowing in fuzzy metric space

Ali, Safa Ezghair; Al-Yaseen, May A. A.

doi:10.47974/JIM-1765

Open Access Research Article

Expansivity and shadowing in fuzzy metric space

^*Safa Ezghair AliCorresponding authorSafa.ali.pure376@student.uobabylon.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonBabylon, IraqView full profile → , May A. A. Al-YaseenPure.may.alaa@uobabylon.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonBabylon, IraqView full profile →

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pp. 753–760Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1765XML

Received:: 17 Oct 2023
Published Online:: 31 May 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1765
Pages:: 753–760

Abstract

We define expansive and topological stability to homeomorphisms on F M - spaces. We offer some basic features of F - expansive homeomorphism. Further, we prove Walter’s theorem in the context from a F M - space, i.e., F- expansive with the F- shadowing feature is F - topologically stable.

Keywords

Fuzzy metric space Continuous triangular norm (t-norm)Expansive Shadowing feature Fuzzy topological stable

Subject Classifications

28E1003E72

References

[1] Badilla, Leonel, et al. “Topological stability for fuzzy expansive maps.” FuzzySets and Systems 425 : 34-47 (2021).
[2] Utz, W. Ro. “Unstable homeomorphisms.” Proceedings of the American Mathematical Society 1.6 : 769-774 (1950).
[3] Michalek, I. Kramosil-J. “Fuzzy metric and statistical metric spaces.” Kybernetika 11.5 : 336-344 (1975).
[4] Ahmadi, Seyyed A., and Mohammad R. Molaei. “Stochastic stability in fuzzy dynamical systems.” Cankaya University Journal of Science and Engineering 9.1 (2012).
[5] A. George and P. Veeramani. “On some results in fuzzy metric spaces.” Fuzzy sets and systems 64.3 : 395-399 (1994).
[6] Sayyari, Y., and M. R. Molaei. “Distal Fuzzy Dynamical Systems.” Applications and Applied Mathematics: An International Journal (AAM) 7.1 : 26 (2012).
[7] Aoki, Nobuo, and Kōichi Hiraide. “Topological theory of dynamical systems: recent advances.” (1994).
[8] Abbood, Mohaimen M., Ebrahim, Hassan H., Al-Fayadh, Ali & Obaid, Ahmed J. () Measure defined on Γ–algebra and some of their generalizations, Journal of Interdisciplinary Mathematics, 1-7, DOI: 10.47974/JIM-1502.
[9] Al-Ameedee, Sarah A. & Obaid, Ahmed J. Sandwich results of meromorphic multivalent functions defined by multiplier transform, Journal of Interdisciplinary Mathematics, OnlineFirst : Latest Articles, 1-8 (2023), DOI: 10.47974/JIM-1484.

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