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On Some Properties of Linear Mappingin Fuzzy Anti n-Normed Spaces

Muhammed Recai Turkmen *, Hakan EFE**

* Faculty of Science and Arts, Mus Alparslan University, Guzeltepe, Turkey.

** Faculty of Science, Gazi University, Teknikokullar, Ankara, Turkey.

Periodicity:October - December'2015
DOI : https://doi.org/10.26634/jmat.4.4.3696

Abstract

In this paper, the authors have studied some properties of continuity and boundedness of linear mapping in fuzzy anti nnormed spaces. Firstly, the authors have given some definitions and theorem, such as fuzzy anti n-normed , fuzzy anti nnormed space and α - n - norms on fuzzy anti n-normed space, convergent sequence and Cauchy sequence on fuzzy anti n-normed space and fuzzy anti-n-Banach space, open ball and closed ball. The authors have presented some examples by using these definitions. Secondly, the authors have studied linear mapping on fuzzy anti n-normed spaces and the authors redefine fuzzy anti n-continuity and fuzzy anti n-bounded by using previous definitions of contiunity and boundedness. Additionally, the authors have given some definitions, weakly fuzzy anti n-continuous, strongly fuzzy anti ncontinuous, sequentially fuzzy anti n-continuous, using these definitions. Moreover, the authors have given the relationship between fuzzy anti n-continuity and fuzzy anti n-boundedness. Finally, the authors have showed that, T is strongly fuzzy anti n-continuous if and only if T is strongly fuzzy anti n-bounded and, T is weakly fuzzy anti n-continuous if and only if T is weakly fuzzy anti n-bounded.

Keywords

N-Normed Spaces, Fuzzy Anti N-Norms, Linear Mapping, Continuity, Boundedness.

How to Cite this Article?

Turkmen, M.R., and Hakan, EFE. (2015). On Some Properties of Linear Mapping in Fuzzy Anti n-Normed Spaces. i-manager’s Journal on Mathematics, 4(4), 9-21. https://doi.org/10.26634/jmat.4.4.3696

References

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[11]. Jebril, I. H. and Samanta, T.K. (2010). “Fuzzy Anti n-normed Space”, Journal of Mathematics and Technology, pp.66- 77.

[12]. M.Recai Turkmen and Hakan Efe (2013). “On Some Properties of Closability of Farthest Point Maps in Fuzzy N-Normed Spaces”, i-manager's Journal on Mathematics, Vol.2(4), Print ISSN 2277-5129, E-ISSN 2277-5137, pp.33-38.

[13]. Bag, T. and Samanta, S.K. (2008). “A Comparative Study of Fuzzy norms on a Linear space”, Fuzzy Sets and Systems, Vol.159, pp.670- 684.

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On Some Properties of Linear Mappingin Fuzzy Anti n-Normed Spaces

Abstract

Keywords

How to Cite this Article?

References

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