Volume 26 • Issue 3 • PP: 49-57 • 2025
Fuzzy Bounded Linear Operators on Fuzzy Anti-Normed Spaces
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The primary goal of this paper is to study and introduce fuzzy anti-normed linear spaces, as well as, some additional properties concerning these spaces. From this point of view, some theoretical results are obtained; for example, it was proved that the space of all linear and fuzzy bounded operators over fuzzy anti-normed linear spaces is fuzzy complete. Moreover, some additional theoretical results are stated and proved.
Keywords
References
[1] C. Felbin, "Finite dimensional fuzzy normed linear space," Fuzzy Sets and Systems, vol. 48, no. 2, pp. 239–248, 1992.
[2] S. C. Cheng and J. N. Mordeson, "Fuzzy linear operators and fuzzy normed linear spaces," in Proc. 1st Int. Conf. Fuzzy Theory and Technology, 1992, pp. 193–197.
[3] S. Sedghi and N. Shobe, "Fixed point theorem in M-fuzzy metric spaces with property (E)," Advances in Fuzzy Mathematics, vol. 1, no. 1, pp. 55–65, 2006.
[4] T. Bag and S. K. Samanta, "Fuzzy bounded linear operators in Felbin's type fuzzy normed linear spaces," Fuzzy Sets and Systems, vol. 159, no. 6, pp. 685–707, 2008.
[5] R. M. Somasundaram and T. Beaula, "Some aspects of 2-fuzzy 2-normed linear spaces," Bull. Malaysian Math. Sci. Soc., vol. 32, no. 2, pp. 211–221, 2009.
[6] M. Janfada, H. Baghani, and O. Baghani, "On Felbin’s-type fuzzy normed linear spaces and fuzzy bounded operators," Iranian Journal of Fuzzy Systems, vol. 8, no. 5, pp. 117–130, 2011.
[7] B. S. Reddy, "Fuzzy anti-2-normed linear space," Journal of Mathematics Research, vol. 3, no. 2, pp. 137–144, 2011.
[8] I. H. Jebril and T. K. Samanta, "Fuzzy anti-normed linear space," Journal of Mathematics and Technology, vol. 26, pp. 338–353, 2010.
[9] B. Dinda, T. K. Samanta, and I. H. Jebril, "Fuzzy anti-norm and fuzzy α-anti-convergence," Demonstratio Mathematica, vol. 45, no. 4, pp. 739–754, 2012.
[10] T. Beaula and B. Maiya, "On fuzzy ward continuity in 2-fuzzy 2-anti normed linear space," International Journal of Engineering, Science and Mathematics, vol. 7, no. 4, pp. 634–639, 2018.
[11] L. D. Kočinac, "Some topological properties of fuzzy anti-normed linear spaces," Journal of Mathematics, vol. 2018, 2018.
[12] P. Sinha, "Fuzzy anti inner product space," International Journal of Applied Engineering Research, vol. 14, no. 19, pp. 3756–3762, 2019.
[13] R. I. Ali and E. A. Hussein, "Some properties of fuzzy anti-inner product spaces," Iraqi Journal of Science, vol. 61, no. 11, pp. 3053–3058, 2020.
[14] G. Rano and T. Bag, "Fuzzy normed linear spaces," International Journal of Mathematics and Scientific Computing, vol. 2, no. 2, pp. 16–19, 2012.
[15] T. Bag and S. K. Samanta, "Finite dimensional fuzzy normed linear spaces," Annals of Fuzzy Mathematics and Informatics, vol. 6, no. 2, pp. 271–283, 2013.
[16] S. Nadaban, "Fuzzy continuous mappings in fuzzy normed linear spaces," International Journal of Computers Communications & Control, vol. 10, no. 6, pp. 74–82, 2015.
[17] F. S. Fadhel, J. H. Eidi, and H. M. Wali, "Contraction mapping theorem in partial fuzzy metric spaces," Journal of Applied Science and Engineering, vol. 25, no. 2, pp. 353–360, 2021.
[18] S. Romaguera and P. Tirado, "Characterizing complete fuzzy metric spaces via fixed point results," Mathematics, vol. 8, no. 2, p. 273, 2020.
[19] I. K. Hanan, F. Al-Taie, F. S. Fadhel, and A. Al-Sabbagh, "Stabilization of fuzzy prey-predator model using backstepping method," Malaysian Journal of Fundamental and Applied Sciences, vol. 20, no. 1, pp. 100–112, 2024.
[20] H. Y. Daher and J. R. Kider, "Some properties of convex fuzzy normed space," International Journal of Mathematics and Computer Science, vol. 19, no. 2, pp. 345–355, 2024.
[21] S. Romaguera and P. Tirado, "On completeness and fixed point theorems in fuzzy metric spaces," Mathematics, vol. 12, no. 2, p. 287, 2024.
[22] S. Romaguera and P. Tirado, "Characterizing complete fuzzy metric spaces via fixed point results," Mathematics, vol. 8, no. 2, p. 273, 2020.
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