Common Fixed Point Results for Self-Mappings in Generalized Fuzzy Cone Metric Spaces

Authors

Keywords:

Common fixed point, Contraction conditions, Fuzzy cone metric space, Weakly compatible, Self mapping

Abstract

A number of generalized contraction results already existed in Cone Metric Space (CMS), Fuzzy Metric Space (FMS) and generalized Fuzzy Cone Metric (FCM) spaces. In the present manuscript, we established some Common Fixed Point (CFP) results in generalized FCM spaces for compatible and weakly compatible self-maps using continuity and without continuity. We establish a new class of Fuzzy Cone Contraction (FCC) theorems extending existing results in the literature including some related examples to these outcomes.

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References

M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, Journal of Mathematical Analysis and Applications 341(1) (2008), 416 – 420, DOI: 10.1016/j.jmaa.2007.09.070.

A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64(3) (1994), 395 – 399, DOI: 10.1016/0165-0114(94)90162-7.

L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications 332(2) (2007), 1468 – 1476, DOI: 10.1016/j.jmaa.2005.03.087.

G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian Journal of Pure and Applied Mathematics 29(3) (1998), 227 – 238.

F. Kiany and A. Amini-Harandi, Fixed point and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces, Fixed Point Theory and Applications 2011 (2011), article number 94, DOI: 10.1186/1687-1812-2011-94.

I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika 11(5) (1975), 336 – 344, URL: https://www.kybernetika.cz/content/1975/5/336/paper.pdf.

T. Öner, Some topological properties of fuzzy cone metric spaces, Journal of Nonlinear Science and Applications 9(3) (2016), 799 – 805, DOI: 10.22436/jnsa.009.03.08.

T. Öner, M. B. Kandemir and B. Tanay, Fuzzy cone metric spaces, Journal of Nonlinear Sciences and Applications 8(5) (2015), 610 – 616, DOI: 10.22436/jnsa.008.05.13.

R. P. Pant, Common fixed points of noncommuting mappings, Journal of Mathematical Analysis and Applications 188(2) (1994), 436 – 440, DOI: 10.1006/jmaa.1994.1437.

B. D. Pant and S. Chauhan, Common fixed point theorems for two pairs of weakly compatible mappings in Menger spaces and fuzzy metric spaces, Scientific Studies and Research. Series Mathematics and Informatics 21(2) (2011), 81 – 96, URL: https://pubs.ub.ro/article/3464.

A. Razani and M. Shirdaryazdi, Some results on fixed points in the fuzzy metric space, Journal of Applied Mathematics and Computing 20 (2006), 401 – 408, DOI: 10.1007/BF02831947.

S. U. Rehman, S. Jabeen, F. Abbas, H. Ullah and I. Khan, Common fixed point theorems for compatible and weakly compatible maps in fuzzy cone metric spaces, Annals of Fuzzy Mathematics and Informatics 19(1) (2020), 1 – 19, DOI: 10.30948/afmi.2020.19.1.1.

S. U. Rehman, Y. Li, S. Jabeen and T. Mahmood, Common fixed point theorems for a pair of self-mappings in fuzzy cone metric spaces, Abstract and Applied Analysis 2019(1) (2019), 2841606, DOI: 10.1155/2019/2841606.

Z. Sadeghi, S. M. Vaezpour, C. Park, R. Saadati and C. Vetro, Set-valued mappings in partially ordered fuzzy metric spaces, Journal of Inequalities and Applications 2014 (2014), article number 157, DOI: 10.1186/1029-242X-2014-157.

B. Schweizer and A. Sklar, Statistical metric spaces, Pacific Journal of Mathematics 10(1) (1960), 385 – 389, DOI: 10.2140/pjm.1960.10.313.

T. Som, Some results on common fixed point in fuzzy metric spaces, Soochow Journal of Mathematics 33(4) (2007), 553 – 561.

M. Suganthi, M. Jayaraman and A. Ramachandran, Generalized contraction theorems in M-fuzzy cone metric spaces, Journal of Innovative Applied Mathematics and Computational Sciences 2(3) (2022), 29 – 40, DOI: 10.58205/jiamcs.v2i3.48.

L. A. Zadeh, Fuzzy sets, Information and Control 8(3) (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.

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Published

30-10-2025

How to Cite

Manjeet, & Singh, R. (2025). Common Fixed Point Results for Self-Mappings in Generalized Fuzzy Cone Metric Spaces. Communications in Mathematics and Applications, 16(3), 793–812. Retrieved from https://www.rgnpublications.com/journals/index.php/cma/article/view/3239

Issue

Vol. 16 No. 3 (2025)

Section

Research Article

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