Characterization on fuzzy soft ordered Banach algebra

Boushra Y. Hussein; Sara F. Hassan

doi:10.5269/bspm.51387

Boushra Y. Hussein Al-Qadisiyah university
Sara F. Hassan Ministry of Education

Abstract

In this paper, we define fuzzy soft ordered Banach algebra with fuzzy soft algebra cone, and introduce the character on fuzzy soft ordered Banach algebra in both cases real and complex. Also, we deduce some of its basic properties and we define a new concept which is a maximal fuzzy soft algebra cone and showing that the set of all fuzzy soft character is isomorphism to the set of all maximal fuzzy soft algebra cone. we prove that the set of all real characters is convex and extreme point, we applied Gelfand- Mazur theorem on fuzzy soft Banach algebra, we showed that character (the set of all complex continuous character) is fuzzy soft ordered Banach algebra. with inverse –closed algebra cone ̆ and a non-zero element in ̆ has inverse we have is an isomorphism to Banach space ( ̆)

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References

Bekir, T., M. Burc Kandemir, Topological Structure of Fuzzy Soft Sets, Computer and Mathematics with Applications, 61, pp. 2952-2957, (2011). https://doi.org/10.1016/j.camwa.2011.03.056

Boushra, Y. H., Sara, F., Real Characterization on Ordered Banach, J. of Advance in mathematics, Vol.9, No.12, (2016). https://doi.org/10.24297/jam.v12i9.126

Dmitri, A. M., Soft Set Theory First Results, Comput. Math. Appl. 37, pp. 19-31, (1999). https://doi.org/10.1016/S0898-1221(99)00056-5

Ildar, S., Solaty, K., Fuzzy Banach Algebra, First Joint Congress on Fuzzy and Intelligent Systems, Ferdorwsi University of Mashhad, Iran, 1.(2007).

Lotfi, Z., Fuzzy Sets, Information and Control, 8, pp. 338- 353 (1965). https://doi.org/10.1016/S0019-9958(65)90241-X

Lebedev, L., Vorovich, I., Gladwell, G., Functional Analysis: Applications in Mechanics and Inverse Problems, 2nd, Ed. Rostov State University, Springer Vol.41, (1996).

Murat, I., Tunay, B., Bayramov, and Cigdem G., A new view on soft normed spaces, International Mathematical Forum, 9, pp. 1149-1159, (2014). https://doi.org/10.12988/imf.2014.4470

Pabitra, M., RoyRanjit, B., Bayramov, and Cigdem G., An Application of Soft Sets in A Decision Making Problem, Comput. Math. Appl. 44, pp. 1077-1083, (2002). https://doi.org/10.1016/S0898-1221(02)00216-X

Pabitra, M., Ranjit, B., Akhil R., Fuzzy Soft Sets, Journal of fuzzy mathematics. Vol. 9, no. 3, pp. 589-602, (2001).

Reza, S., Seyed, M. V., Some Results on Fuzzy Banach Spaces, J. Appl. Math. Comput., 17, pp. 1-2, (2005). https://doi.org/10.1007/BF02936069

Sujoy, D., Pinaki, M., Syamal, On Soft Linear Spaces and Soft Normed Linear Spaces, Ann. Fuzzy Math. Inform. 9, pp. 91-109, (2015).

Sonja, M., A Spectral Problem in Ordered Banach Algebras, Bull. Austral Math., Soc. 67, pp. 131-144, (2003). https://doi.org/10.1017/S0004972700033591

Thangaraj, B. and Nirmal, K. M., A New Notion for Fuzzy soft Normed Linear Space, Intern. J. Fuzzy Mathematical Archive, Vol. 9, No. 1., pp. 81-90, (2015).

Thakur, R. and Samanta, S., Soft Banach Algebra, Ann. Fuzzy Mathematics and inf., 10, pp. 397-412, (2015).

Tudor, B., Ftavius, P., Sorin N., On fuzzy normed algebra, J. Nonlinear Sci. Appl. 9 (2016).

Walter, R., Functional Analysis, 2nd. Ed. University Wisconsin (1991).

Zdzis law, P., Rough sets, Int. J. Comput. Sci. 11(1982), pp. 341-536. https://doi.org/10.1007/BF01001956