Fuzzy Open Mapping and Fuzzy Closed Graph Theorems in Fuzzy Length Space
Abstract
The theory of fuzzy set includes many aspects that regard important and significant in different fields of science and engineering in addition to there applications. Fuzzy metric and fuzzy normed spaces are essential structures in the fuzzy set theory. The concept of fuzzy length space has been given analogously and the properties of this space are studied few years ago. In this work, the definition of a fuzzy open linear operator is presented for the first time and the fuzzy Barise theorem is established to prove the fuzzy open mapping theorem in a fuzzy length space. Finally, the definition of a fuzzy closed linear operator on fuzzy length space is introduced to prove the fuzzy closed graph theorem.
Downloads
References
[2] I. Kramosil and J. Michalek, “Fuzzy metric and statistical metric space”, Kybernetica, 11(1975), pp: 326-334.
[3] A. George and P. Veeramani," On Some Results in Fuzzy Metric Spaces", Fuzzy Sets and Systems, 64(1994), pp: 395-399.
[4] A.K. Katsaras, “Fuzzy topological vector spaces”, Fuzzy Sets and Systems, 12(1984), pp:143- 154.
[5] C.Felbin, "Finite-dimensional fuzzy normed linear spaces", Fuzzy Sets and Systems, Vol. 48 ( 1992 ), pp: 239-248.
[6] T.Bag, "Some Fundamental Theorems in Felbin’s Type Fuzzy Normed Linear Spaces", international journal of mathematics and scientific computing, vol. 1, 2(2011), pp:44-49.
[7] M. Saheli, A. Hasankhani, and A. Nazari,"Some Properties of Fuzzy Norm of Linear Operators", Iranian Journal of Fuzzy Systems, Vol. 11, No. 2 (2014), pp: 121-139.
[8] T.Bag and S.Samanta, "Some fixed point theorems in fuzzy normed linear spaces", Information sciences, Vol.177(2007), pp:3271-3289.
[9] T.Bag and S.Samanta," Fixed point theorems on Fuzzy normed spaces", Inf. sci. Vol.176 (2006), pp:2910-2931.
[10] M. Goudarzi and S. Vaezpour, "Best simultaneous approximation in fuzzy normed spaces", Iranian J. of Fuzzy Systems, Vol.7(2010),87-69.
[11] C.Alegre and S.Romaguera, " On the uniform boundedness theorem in fuzzy quasi-normed spaces", Fuzzy Sets and Systems. , Vol. 282(2016), pp: 143-153.
[12] J. Kider and J.Mousa, "Properties of Fuzzy Length on Fuzzy Set", Open Access Library Journal, Vol. 3, November 17( 2016), pp:1-13.
[13] U. Gozutok and Y. Sagıroglu," On Fuzzy Length Spaces and Fuzzy Geodesics", International Journal of Advanced Engineering Research and Science (IJAERS), Vol.4(2017), pp:200-202.
[14] J. Kider and J.Mousa,"The Fuzzy Length of Fuzzy Bounded Operator", Iraqi Journal of Science, Vol. 58(2017), pp: 284-291.
[15] J.Mousa, "Properties of Fuzzy Length on Fuzzy Set", M.Sc. Thesis 2016, University of Technology, Iraq.
Copyright © Author(s) . This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
