|
|
Pure Mathematics 2024
模糊赋范Riesz空间上模糊算子的研究
|
Abstract:
本文在模糊赋范Riesz空间中引入-α范数，给出弱模糊范数有界线性泛函的定义。研究了模糊序有界线性泛函与弱模糊范数有界线性泛函之间的关系。在模糊Banach格上，模糊序有界线性泛函和弱模糊范数有界线性泛函是等价的。
In this paper, α-norm is introduced in fuzzy normed Riesz space, and the definition of fuzzy weak norm bounded linear functional is given. The relationship between fuzzy ordered bounded linear functionals and fuzzy weakly norm bounded linear functionals is studied. On fuzzy Banach lattices, fuzzy order bounded linear functionals and fuzzy weak norm bounded linear functionals are equivalent.
| [1] | Zadeh, L.A. (1965) Fuzzy Sets. Information Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X |
| [2] | Zadeh, L.A. (1971) Similarity Relations and Fuzzy Orderings. Information Sciences, 3, 177-200. https://doi.org/10.1016/S0020-0255(71)80005-1 |
| [3] | Katsaras, A.K. (1984) Fuzzy Topological Vector Spaces I. Fuzzy Sets Systems, 6, 85-95. https://doi.org/10.1016/0165-0114(81)90082-8 |
| [4] | Venugopalan, P. (1992) Fuzzy Ordered Sets. Fuzzy Sets and Systems, 46, 221-226. https://doi.org/10.1016/0165-0114(92)90134-P |
| [5] | Felbin, C. (1992) Finite Dimensional Fuzzy Normed Linear Space. Fuzzy Sets Systems, 48, 239-248. https://doi.org/10.1016/0165-0114(92)90338-5 |
| [6] | Beg, I. and Islam, M.U. (1995) Fuzzy Ordered Linear Spaces. Fuzzy Mathematics, 3, 659-670. |
| [7] | Beg, I. and Islam, M.U. (1994) Fuzzy Riesz Spaces. Fuzzy Mathematics, 2, 211-228. https://doi.org/10.1142/9789814447010_0001 |
| [8] | Bag, T. and Samanta, S.K. (2003) Finite Dimensional Fuzzy Normed Linear Spaces. Fuzzy Mathematics, 11, 687-705. |
| [9] | Bag, T. and Samanta, S.K. (2005) Fuzzy Bounded Linear Operators. Fuzzy Sets and Systems, 151, 513-547. https://doi.org/10.1016/j.fss.2004.05.004 |
| [10] | Hong, L. (2015) Fuzzy Riesz Subspaces, Fuzzy Ideals, Fuzzy Bands, and Fuzzy Band Projections. Seria Matematica- Informatica, 53, 77-108. https://doi.org/10.1515/awutm-2015-0005 |
| [11] | Park, C., Movahednia, E., Mosadegh, S.M.S.M., et al. (2018) Riesz Fuzzy Normed Spaces and Stability of a Lattice Preserving Functional Equation. Journal of Computational Analysis Applications, 24, 569-579. |
| [12] | Iqbal, M. and Bashir, Z. (2020) The Existence of Fuzzy Dedekind Completion of Archimedean Fuzzy Riesz Space. Computational and Applied Mathematics, 39, 116. https://doi.org/10.1007/s40314-020-1139-3 |
| [13] | Guirao, J., Iqbal, M., Bashir, Z., et al. (2021) A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces. Mathematics, 9, 1512. https://doi.org/10.3390/math9131512 |
| [14] | Bashir, Z. and Iqbal, M. (2022) The Unbounded Fuzzy Norm Convergence in Fuzzy Banach Lattices. Soft Computing, 26, 25-31. https://doi.org/10.1007/s00500-021-06437-2 |
| [15] | 赵家锐, 李浩, 潘相宇. 模糊赋范Riesz空间的性质[J]. 应用数学进展, 2022, 11(4): 2017-2023. |
| [16] | 陈强, 周姮媛, 刘艳丽. 模糊Riesz空间上模糊序有界线性算子的研究[J]. 理论数学, 2024, 14(3): 74-82. |
| [17] | Zaanen, A.C. (1997) Introduction to Operator Theory in Riesz Spaces. Springer, Berlin Heidelberg. https://doi.org/10.1007/978-3-642-60637-3 |
