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The algebra fuzzy norm of the quotient space and pseudo algebra fuzzy normed space | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3589-3597 اصل مقاله (406.3 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6139 | ||
| نویسندگان | ||
| Zainab A. Khudhair* 1؛ Jehad Rmadhan Kider2 | ||
| 1Branch of Mathematics and Computer Applications, Department of Applied Sciences, University of Technology, Baghdad, Iraq | ||
| 2Branch oh Mathematics and Computer Applications, School of Applied Sciences, University of Technology, Iraq. | ||
| تاریخ دریافت: 23 اردیبهشت 1400، تاریخ بازنگری: 30 شهریور 1400، تاریخ پذیرش: 24 مهر 1400 | ||
| چکیده | ||
| The principle aim of this article is to use the notion of algebra fuzzy normed space and its basic properties in order to introduce the notion of algebra fuzzy norm of the quotient space. If the quotient space is fuzzy complete then we prove that U is fuzzy complete. Also, we introduce the notion of pseudo algebra fuzzy normed space and investigate the basic properties of this space. In this direction we define a relation $\sim $ on $ U $ in order to introduce the space $\widehat{{U}}$ of classes $\widehat{ u } =[u]= \{z \in U: z \sim u \} $. If U is pseudo algebra fuzzy normed space then we prove that $\widehat{{U}}$ is algebra fuzzy normed space also if U is a fuzzy complete we prove that $\widehat{{U}}$ is fuzzy complete. | ||
| کلیدواژه‌ها | ||
| Algebra fuzzy absolute space؛ Algebra fuzzy normed space؛ Fuzzy complete؛ Fuzzy bounded linear operator | ||
| مراجع | ||
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[1] I. Sadeqi and F. Kia, Fuzzy normed linear space and its topological structure, Chaos Solutions Fractals 40(5) (2009) 2576–2589. [2] J.R. Kider, On fuzzy normed spaces, Eng. Tech. J. 29(9) (2011) 1790–1795. [3] J.R. Kider, Completion of fuzzy normed spaces, Eng. Tech. J. 29(10) (2011) 2004–2012. [4] J.R. Kider, New fuzzy normed spaces, J. Baghdad Sci. 9 (2012) 559–564. [5] T. Bag and S. Samanta, Finite dimensional fuzzy normed spaces, Ann. Fuzzy Math. Inf. 6(2) (2013) 271–283. [6] J.R. Kider and N. Kadhum, Properties of fuzzy norm of fuzzy bounded operators, Iraqi J. Sci. 58(3A) (2017) 1237–1281. [7] N. Kadhum, On Fuzzy Norm of a Fuzzy Bounded Operator on Fuzzy Normed Spaces, M.Sc. Thesis University of Technology, Iraq, 2017. [8] A. Ali, Properties of Complete Fuzzy Normed Algebra, M.Sc. Thesis University of Technology, Iraq, 2018. [9] J.R. Kider and A. Ali, Properties of fuzzy absolute value on and properties finite dimensional fuzzy normed space, Iraqi J. Sci. 59(2B) (2018) 909–916. [10] J.R. Kider and M. Gheeab, Properties of a general fuzzy normed space, Iraqi J. Sci. 60(4) (2019) 847–855. [11] J.R. Kider and M. Gheeab, Properties of the space GFB(V, U), J. AL-Qadisiyah Somput. Sci. Math. 11(1) (2019) 102–110. [12] J.R. Kider and N. Kadhum, Properties of fuzzy compact linear operators on fuzzy normed spaces, Baghdad Sci. J. 16(1) (2019) 104–110. [13] J.R. Kider, Some properties of fuzzy soft metric space, Al-Qadisiyah J. Pure Sci. 25(2) (2020) 1–13. [14] J.R. Kider, Some properties of algebra fuzzy metric space, J. Al-Qadisiyah Comput. Sci. Math. 12(2) (2020) 43–56. [15] J.R. Kider and M. Gheeab, Properties of the adjoint operator of a general fuzzy bounded operator, Baghdad Sci. J. 18(1) (2021) 790–796. [16] Z.A. Khudhair and J.R. Kider, Some properties of algebra fuzzy absolute value space and algebra fuzzy normed space, Al-Qadisiyah J. Pure Sci. 25(4) (2020) 46–58. | ||
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