Bounded Linear Transformations in G-Fuzzy Normed Linear Space
DOI:
https://doi.org/10.29304/jqcm.2021.13.1.756Keywords:
G-norm, bounded transformation, G-fuzzy norm, continuous functions, G-fufuzzy normed linear space.Abstract
In a host of mathematical applications, the bounded linear transformation arises. The aim of the present work is to report the definition of continuous for linear transformation by using the idea of G-fuzzy normed linear space (GFNLS) with proving the main theorem regarding the continuity. Besides, the notion of a bounded linear transformation depending on GFNLS is presented and some basic properties related to this notion are proved. Furthermore, the extension of a bounded linear transformation is discussed and proved. Finally, a characterization for the notion G-B(X,Y) which is consisting of all bounded linear transformations is presented and proved that this characterization is a complete GFNLS if the space Y is complete.
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References
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[2] Z. Mustafa and B. Sims, "Some remarks concerning D-metric space", Proceedings of the International Conferences on Fixed Point Theory and Applications”, Valencia (Spain), (2003), pp. 189-198.
[3] Z. Mustafa, and B. Sims, "A new approach to generalized metric spaces", Journal of Nonlinear and convex Analysis, vol. 7 (2), (2006), pp. 289-297.
[4] G. Sun and K. Yang, "Generalized fuzzy metric spaces with properties", Research Journal of Applied Sciences, Engineering and Technology, vol. 2 (7), (2010), pp. 673-678.
[5] A. F. Sayed, A. Alahmari and S. Omran, "On Fuzzy Soft G-Metric Spaces", Journal of Advances in Mathematics and Computer Science, vol. 27 (6), (2018), pp. 1-15.
[6] M. Jeyaraman, R. Muthuraj, M. Sornavalli and Z. Mustafa, "Common Fixed Point Theorems for W-Compatible maps of type (P) in Intuitionistic Generalized Fuzzy Metric Spaces", International Journal of Advances in Mathematics, vol. (5), (2018), pp. 34-44.
[7] M. Rajeswari and M. Jeyaraman, "Fixed Point Theorems for Reciprocally Continuous Maps in Generalized Intuitionistic Fuzzy Metric Spaces", Advances in Mathematics, Scientific Journal, vol. 8 (3), (2019), pp. 73–78.
[8] K. A. Khan, "Generalized normed spaces and fixed point theorems", Journal of Mathematics and Computer Science, vol. 13, (2014), pp. 157-167.
[9] S. Chatterjee, T. Bag and S. K. Samanta, "Some results on G-fuzzy normed linear space", Int. J. Pure Appl. Math., vol. 120 (5), (2018), pp. 1295–1320.
[10] M. Khanehgir, M. M. Khibary, F. Hasanvanda, A. Modabber, "Multi-Generalized 2-Normed Space", Published by Faculty of Sciences and Mathematics, vol. 31 (3), (2017), pp. 841–851.
[11] J. Xiao and X. Zhu, "Fuzzy normed spaces of operators and it is completeness", Fuzzy sets and Systems, vol. 133, (2004), pp.437-452.
[12] B. Lafuerza-Guillén, J. A. Rodríguez-Lallena and C. Sempi, "A study of boundedness in probabilistic normed spaces", J. Math. Anal. Appl., vol. 232, (1999), pp. 183–196.
[13] I. Sadeqi, and F. S. Kia, "Fuzzy normed linear space and its topological structure", Chaos Solitons Fractals, vol. 40, (2009), pp. 2576–2589.
[14] A. Szabo, T. Bînzar, S. N˘ad˘aban and F. Pater, "Some properties of fuzzy bounded sets in fuzzy normed linear space", In Proceedings of the AIP Conference Proceedings, Thessaloniki, Greece, 25–30 September (2017); AIP Publishing: Melville, NY, USA; Vol. 1978.
[15] A. Szabo, T. Bînzar, S. Nădăban and F. Pater, "Some properties of fuzzy bounded sets in fuzzy normed linear spaces", AIP Conference Proceedings 1978, 390009, (2018), https://doi.org/10.1063/1.5043993.
[16] N. F. Al-Mayahia, and D. S. Farhood, "Separation Theorems For Fuzzy Soft normed space." Journal of Al-Qadisiyah for computer science and mathematics, vol. 11 (3), (2019), p. 89.
[17] B. T. Bilalov, S. M. Farahani and F. A. Guliyeva, "The Intuitionistic Fuzzy Normed Space of Coefficients", Abstract and Applied Analysis, Article ID 969313, 11 pages, (2012), https://doi.org/10.1155/2012/969313.
[18] T. Bag and S. Samanta, "Fuzzy bounded linear operators", Fuzzy sets and Systems, vol. 151 (3), (2005), pp. 513-547.
[19] J. Zhao, C. M. Lin and F. Chao, "Wavelet Fuzzy Brain Emotional Learning Control System Design for MIMO Uncertain Nonlinear Systems", Front. Neurosci, vol. 12, (2018), pp. 918.
[20] M. Janfada, H. Baghani and O. Baghani, "ON FELBIN’S-TYPE FUZZY NORMED LINEAR SPACES ANDFUZZY BOUNDED OPERATORS", Iranian Journal of Fuzzy Systems, vol. 8 (5), pp. 117-130.
[21] K. Nomura, "Linear transformations that are tridiagonal with respect to the three decompositions for an LR triple", Linear Algebra and its Applications, vol. 486, (2015), pp. 173-203.
[22] P. Sinha, G. Lal and D. Mishra, "Fuzzy 2-Bounded Linear Operators,” International Journal of Computational Science and Mathematics", vol. 7 (1), (2015), pp. 1-9.
[23] S. Chatterjee, T. Bag and S. K. Samanta, "Some Fixed Point Theorems in G-fuzzy Normed Linear Spaces", Recent Advances in Intelligent Information Systems and Applied Mathematics, (2020), 87-101.
[24] T. Bag and S. Samanta, "Finite dimensional fuzzy normed linear spaces", J. Fuzzy Math. Vol. 11 (3), (2003), pp. 687-705.
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Published
2021-02-25
How to Cite
Mohammedali, M. N., & Sabri, R. I. (2021). Bounded Linear Transformations in G-Fuzzy Normed Linear Space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(1), Math Page 110– 119. https://doi.org/10.29304/jqcm.2021.13.1.756
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Math Articles
