Compatible Mappings of Type (K) in Fuzzy Metric Space

Authors

  • Nandu Prasad Koiri Department of Mathematics, Tri-Chandra Multiple Campus, Tribhuvan University, Nepal
  • Ajay Kumar Chaudhary Department of Mathematics, Tri-Chandra Multiple Campus, Tribhuvan University, Nepal https://orcid.org/0000-0002-0015-7695
  • Rajeev Kumar Department of Mathematics, Arunodaya University, Itanagar, Arunachal, India
  • K. B. Manandhar Department of Mathematics, School of Science, Kathmandu University, Nepal

DOI:

https://doi.org/10.3126/jist.v30i1.76304

Keywords:

Common fixed point, compatible mappings, compatible mappings of type (K), Fuzzy metric space

Abstract

This paper discusses common fixed-point theorem in fuzzy metric space for three self-mappings by using the conditions of compatible mappings of type (K). This theorem generalizes the results of K.B. Manandhar et al. (2014), and also the results of Cho (2006).

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References

Balasubramaniam, P., Muralisankar, S., & Pant, R.P. (2002). Common fixed points of four mappings in a fuzzy metric space. The Journal of fuzzy mathematics, 10(2), 379-384.

Chaudhary, A.K., Manandhar, K.B., Jha, K., & Murthy, P.P. (2021). A common fixed point theorem in Menger space with compatible mapping of type (P). International Journal of Mathematical Sciences & Applications, 15(2), 59-70.

Chaudhary, A.K. (2023). Occasionally weakly compatible mappings and common fixed points in Menger space. Results in Nonlinear Analysis, 6(4), 47–54.

Chauhan, S.S. (2009). Common fixed-point theorem for two pairs of weakly compatible mappings in M-fuzzy metric spaces. International Journal of Mathematical Analysis, 3(8), 393-398.

Cho, S.H. (2006). On common fixed points in fuzzy metric spaces. International Mathematical Forum, 1(10), 471-479.

Cho, S.H., & Jung, J.H. (2006). On common fixed Point theorems in fuzzy metric spaces. International Mathematical Forum, 1, 1441-1451.

Cho, S.H. (2006). On common fixed-point theorems in fuzzy metric spaces. Journal of Applied Mathematics and Computing, 20(1-2), 523-533.

Cho, Y.J., Pathak, H.K., Kang S.M., & Jung, J.S. (1998). Common fixed points of compatible maps of type (P) on fuzzy metric spaces. Fuzzy Sets and System, 93, 99-111.

Fr´echet, M. (1906). Sur quelques points du calcul fonctionnel, Th`ese, Paris, 1905. Rendiconti del Circolo Matematico di Palermo, 22, 1–74.

George, A., & Veeramani, P. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64, 395-399.

George, A., & Veeramani, P. (1997). On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90, 365-368.

Grabiec, M. (1988). Fixed points in fuzzy metric Spaces. Fuzzy Sets and Systems, 27(3), 385- 389.

Gregori, V., & Sapena, A. (2002). On fixed point theorems in fuzzy metric spaces. Fuzzy sets and Systems, 125, 245-252.

Heilpern, S. (1981). Fuzzy mappings and fixed point theorem. Journal of Mathematical Analysis and Applications, 83(2), 566–569.

Jain, S., Mundra, B., & Aske, S. (2009). Common fixed point theorem in fuzzy metric space using implicit relation. International Mathematical Forum, 4(3), 135-141.

Jha, K. (2010). A common fixed-point theorem for sequence of mapping in fuzzy metric space. The Journal of Fuzzy Mathematics, 3, 1-7.

Jha, K. (2013). A common fixed-point theorem for semi compatible maps in fuzzy metric space. Kathmandu University Science, Engineering and Technology, 9, 83-89.

Jungck, G. (1986). Compatible mappings and fixed points, International Journal of Mathematical Sciences, 9(4), 771-779.

Jungck, G., Murthy, P.P., & Cho, Y.J. (1993). Compatible mappings of type (A) and common fixed points. Mathematica Japonica, 38(2), 381-390.

Klement, E.P., Mesiar, R., & Pap, E. (2004). Triangular norms, positional paper. Fuzzy Sets and Systems, 143(1), 5-26.

Kramosil, I., & Michalek, J. (1975). Fuzzy metric and statistical metric spaces. Kybernetika, 11, 336-344.

Kumar, S., & Fisher, B. (2011). A common fixed point theorem in fuzzy metric space using property (E.A.) and implicit relation. Thai Journal of Mathematics, 9, 21-28.

Manandhar, K.B., Jha, K., & Porru, G. (2014). Common fixed-point theorem of compatible Mappings of type (K) in fuzzy metric spaces. Electronic Journal of Mathematical Analysis and Applications, 2(2), 248-253.

Manandhar, K.B., Jha, K., & Pathak, H.K. (2014). A common fixed-point theorem for compatible mappings of type (E) in fuzzy metric space. Applied Mathematical Sciences, 8, 207- 214.

Mishra, S.N., Sharma, N., & Singh, S.L. (1994). Common fixed points of maps on fuzzy metric spaces. International Journal of Mathematics and Mathematical Sciences, 17(2), 253–258.

Mishra, U., Ranadive, A.S., & Gopal, D. (2008). Some fixed-point theorems in fuzzy metric spaces. Tamkang Journal of Mathematics, 39(4), 309-316.

Pant, R.P., & Jha, K. (2004). A remark on common fixed points of four mappings in a fuzzy metric space. The Journal of fuzzy mathematics, 12(2), 433-437.

Pathak, H.K., Cho, Y.J., Chang, S.S., & Kang, S.M. (1996). Compatible mappings of type (P) and fixed point theorems in metric spaces and probabilistic metric spaces. Novi Sad Journal of Mathematics, 26, 87-109.

Pathak, H.K., Cho, Y.J., Kang, S.M., & Madharia, B. (1998). Compatible mappings of type(C) and common fixed-point theorems of Gregu´s type. Demonstratio Mathematica, 31(3), 499-518.

Pathak, H.K., & Khan, M.S. (1995). Compatible mappings of type (B) and common fixed point theorems of Gregu´s type. Czechoslovak Mathematical Journal, 45(4), 685-698.

Rohen, Y., & Singh, M.R. (2008). Common fixed point of compatible mappings of type (R) in complete metric spaces. International Journal of Mathematical Sciences and Engineering Applications, 2(4), 295- 303.

Schweizer, B., & Sklar, A. (1960). Statistical metric spaces. Pacific Journal of Mathematics, 10(1), 313-334.

Sessa, S. (1982). On weak commutativity condition of mappings in fixed point considerations. Publications de l'Institut Mathématique (Beograd), 32(46), 149-153.

Singh, B., & Chauhan, M.S. (2000). Common fixed points of compatible maps in fuzzy metric spaces. Fuzzy Sets and Systems, 115, 471-475.

Singh, M.R., & Singh, Y.M. (2007). Compatible mappings of type (E) and common fixed point theorems of Meir-Keeler type. International Journal of Mathematical Sciences and Engineering Applications, 1, 299–315.

Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8, 338-353.

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Published

2025-06-28

How to Cite

Koiri, N. P., Chaudhary, A. K., Rajeev Kumar, & Manandhar, K. B. (2025). Compatible Mappings of Type (K) in Fuzzy Metric Space. Journal of Institute of Science and Technology, 30(1), 237–242. https://doi.org/10.3126/jist.v30i1.76304

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Section

Research Articles