Fuzzy Continuous Mappings in Fuzzy Normed Linear Spaces
Keywords:
Fuzzy normed linear spaces, fuzzy continuous mapping, fuzzy bounded linear operatorsAbstract
In this paper we continue the study of fuzzy continuous mappings in fuzzy normed linear spaces initiated by T. Bag and S.K. Samanta, as well as by I. Sadeqi and F.S. Kia, in a more general settings. Firstly, we introduce the notion of uniformly fuzzy continuous mapping and we establish the uniform continuity theorem in fuzzy settings. Furthermore, the concept of fuzzy Lipschitzian mapping is introduced and a fuzzy version for Banach’s contraction principle is obtained. Finally, a special attention is given to various characterizations of fuzzy continuous linear operators. Based on our results, classical principles of functional analysis (such as the uniform boundedness principle, the open mapping theorem and the closed graph theorem) can be extended in a more general fuzzy context.References
Alegre, C., Romaguera, S. (2010); Characterizations of fuzzy metrizable topological vector spaces and their asymmetric generalization in terms of fuzzy (quasi-)norms, Fuzzy Sets and Systems, 161(16): 2181-2192. http://dx.doi.org/10.1016/j.fss.2010.04.002
Bag, T., Samanta, S.K. (2003); Finite dimensional fuzzy normed linear spaces, Journal of Fuzzy Mathematics, 11(3): 687-705.
Bag, T., Samanta, S.K. (2005); Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151: 513-547. http://dx.doi.org/10.1016/j.fss.2004.05.004
Chang, C.L. (1968); Fuzzy topological spaces, J. Math. Anal. Appl., 24: 182-190. http://dx.doi.org/10.1016/0022-247X(68)90057-7
Cheng, S.C., Mordeson, J.N. (1994); Fuzzy linear operator and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 86: 429-436.
Felbin, C. (1992); Finite dimensional fuzzy normed liniar space, Fuzzy Sets and Systems, 48: 239-248. http://dx.doi.org/10.1016/0165-0114(92)90338-5
Goleţ, I. (2010); On generalized fuzzy normed spaces and coincidence point theorems, Fuzzy Sets and Systems, 161(8): 1138-1144. http://dx.doi.org/10.1016/j.fss.2009.10.004
Katsaras, A.K. (1984); Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12: 143-154. http://dx.doi.org/10.1016/0165-0114(84)90034-4
Kramosil I., Michálek, J. (1975); Fuzzy metric and statistical metric spaces, Kybernetica, 11: 326-334.
Nădăban, S., Dzitac, I. (2014); Atomic Decompositions of Fuzzy Normed Linear Spaces for Wavelet Applications, Informatica, 25(4): 643-662.
Nădăban, S. (2014); Fuzzy pseudo-norms and fuzzy F-spaces, Fuzzy Sets and Systems, doi: 10.1016/j.fss.2014.12.010. http://dx.doi.org/10.1016/j.fss.2014.12.010
Sadeqi, I., Kia, F.S. (2009); Fuzzy normed linear space and its topological structure, Chaos, Solitons and Fractals, 40(5): 2576-2589. http://dx.doi.org/10.1016/j.chaos.2007.10.051
Schweizer, B., Sklar, A. (1960); Statistical metric spaces, Pacific J. Math., 10: 314-334.
Zadeh, L.A. (1965); Fuzzy sets, Information and Control, 8: 338-353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
Published
Issue
Section
License
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.