SOME RESULTS IN SOFT COMPACT FUZZY METRIC SPACES AND ITS APPLICATIONS

Year 2022, , 1 - 10, 31.12.2022

Akhlak Mansurı , Vipin Kumar Sharma

https://doi.org/10.54559/jauist.1089062

Abstract

In this paper we introduced basic notions of soft sets and examined some important properties of soft metric and soft fuzzy metric spaces. The main object of this research article to establish some coincidence point theorems in soft compact fuzzy metric spaces and its applications.

Keywords

Soft fuzzy metric space, soft element, soft set, soft mappings, soft continuous mapping, soft contractive mapping, fixed point theorem.

References

• [1] Abbas, M., Altun, I., Gopal, D. (2009). Common fixed-point theorems for non-compatible mappings in fuzzy metric spaces, Bull. Math. Anal. Appl., 1(2), 47–56.
• [2] Ali, M.I., Feng, F., Liu, X., Min, W.K. and Shabir, M. (2005). on some new operations in soft set theory, Comput. Math. Appl.49,1547-1553.
• [3] Al-Thagafi, M.A., Shahzad, N. (2009). A note on occasionally weakly compatible maps, Int. Journal of Math. Analysis, 3(2), 55–58.
• [4] Beg, I., Gupta, V., Kanwar, A. (2015). Fixed Point on Intuitionistic Fuzzy Metric Spaces Using E.A. Property, Journal of Nonlinear Functional Analysis, 2015, Article ID 20.
• [5] Branciari, A. (2002). A fixed-point theorem for mappings satisfying a general contractive condition of integral type, International Journal of Mathematics and Mathematical Sciences, 29, 531 –536.
• [6] Chen, D. (2005). The parameterization reduction of soft sets and its applications, Comput. Math. Appl. 49 757-763.
• [7] Das, S., Samanta, S. K. (2012). Soft real sets, soft real numbers and their properties, J. Fuzzy Math. 20 (3) 551-576. [8] Das, S., Samanta, S. K. (2013). Soft metric, Annals of Fuzzy Mathematics and Informatics, 6(1) 77-94.
• [9] Das, S., Samanta, S. K. (2013). On soft metric spaces, J. Fuzzy Math, 21(3).
• [10] George, A. and Veeramani, P. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems 64, 395–399.
• [11] Gunduz, C. On Soft Mappings, arXiv: 1305.4545v1 [math.GM], 16 May 2013.
• [12] Gupta, V., Kanwar, A. (2012). Fixed Point Theorem in Fuzzy Metric Spaces Satisfying E.A Property, Indian Journal of Science and Technology, 5(12) 3767–3769.
• [13] Hussain, S., Ahmad, B. (2011). Some properties of soft topological spaces, Computers and Math. with Applications, 62, 4058-4067.
• [14] Kramosil, I., Michalek, J. (1975). Fuzzy metric and statistical spaces. Kybernetica 11, 336–344.
• [15] Long-Guang, H., Xian, Z. (2007). Cone metric spaces and fixed-point theorems of contractive mappings, J. Math. Anal. Appl. 332,1468-1476.
• [16] (2002). An application of soft sets in a decision-making problem, Comput. Math. Appl.44, 1077-1083.
• [17] Maji, P. K., Biswas, R., Roy, A.R. (2003). Soft set theory, Comput. Math. Appl.45 555-562.
• [18] Majumdar, P. and Samanta, S. K. (2010). On soft mappings, Comput. Math. Appl. 60, 2666-2672.
• [19] Mishra, S.N., Singh, S.L (1994). Common fixed points of maps in fuzzy metric space, Int. J. Math. Math. Sci., 17(2), 253–258.
• [20] Molodtsov, D. (1999). Soft set-theory-first results, Comput. Math. Appl.37,19-31.
• [21] Rhoades, B.E. (1977). A comparison of various definition of contractive mappings, Trans. Amer. Math. Soc. 266 257-290. [22] Saini, R.K., Gupta, V., Singh, S.B., Kumar, M. (2008). Common coincidence Points of R-Weakly Commuting Fuzzy Maps, Thai Journal of Mathematics,6(1), 109–115.
• [23] Shabir, M., Naz, M. (2011). on soft topological spaces, Comput. Math. Appl.61,1786-1799. [24] Singh, B., Chouhan, M.S. (2000). Common fixed points of compatible maps in fuzzy metric spaces, Fuzzy Sets and Systems, 115(3), 471–475.
• [25] Singh, B., Jain, S. (2005). Semi-compatibility and fixed-point theorems in fuzzy metric space using implicit relation, Int. J. Math. Math. Sci., 2005(16), 2617–2629.
• [26] Singh, B., Jain, S. (2005). Weak compatibility and fixed points in fuzzy metric spaces, Ganita, 56(2), 167–176.
• [27] Som, T. (2007). Some Results on Common fixed point in Fuzzy Metic Spaces, Soochow J. Math., 33(4), 553–561.
• [28] Subrahmanyam, P.V. (1995). A common fixed-point theorem in fuzzy metric spaces, Information Sciences, 83(3-4), 109-112.
• [29] Zadeh, L.A. (1965). Fuzzy Sets, Information and control, 8(3), 338–353.