In this paper, I study to expand homomorphisms on fuzzy Banach algebra based on Jensen-type functional equation with 2k-variable. First, we study extended homomorphisms on fuzzy Banach algebra with the fixed point method. Next, we study extended homomorphism on fuzzy Banach algebra by direct method. These are the main results of this paper.
Cite this paper
An, L. V. (2023). Building Extended Homomorphism on Fuzzy Banach Algebra Based on Jensen Equation with 2k-Variables by Fixed Point Methods and Direct Methods. Open Access Library Journal, 10, e206. doi: http://dx.doi.org/10.4236/oalib.1110206.
Hyers, D.H. (1941) On the Stability of the Functional Equation. Proceedings of the National Academy of the United States of America, 27, 222-224.
https://doi.org/10.1073/pnas.27.4.222
Cheng, S.C. and Mordeson, J.M. (1994) Fuzzy Linear Operators and Fuzzy Normed Linear Spaces. Bulletin of the Calcutta Mathematical Society, 86, 429-436.
Mirmostafaee, A.K. and Moslehian, M.S. (2008) Fuzzy Versions of Hyers-Ulam-Rassias Theorem. Fuzzy Sets and Systems, 159, 720-729.
https://doi.org/10.1016/j.fss.2007.09.016
Mirmostafaee, A.K. and Moslehian, M.S. (2008) Fuzzy Approximately Cubic Mappings. Information Sciences, 178, 3791-3798.
https://doi.org/10.1016/j.ins.2008.05.032
Mirmostafaee, A.K., Mirzavaziri, M. and Moslehian, M.S. (2008) Fuzzy Stability of the Jensen Functional Equation. Fuzzy Sets and Systems, 159, 730-738.
https://doi.org/10.1016/j.fss.2007.07.011
Aoki, T. (1950) On the Stability of the Linear Transformation in Banach Spaces, on the Stability of the Linear Transformation in Banach Spaces. Journal of the Mathematical Society of Japan, 2, 64-66. https://doi.org/10.2969/jmsj/00210064
Czerwik, S. (1992) On the Stability of the Quadratic Mapping in Normed Spaces. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 62, 59-64. https://doi.org/10.1007/BF02941618
Eshaghi Gordji, M. and Bavand Savadkouhi, M. (2009) Approximation of Generalized Homomorphisms in Quasi-Banach Algebras. Analele Stiintifice ale Universitatii Ovidius Constanta, 17, 203-214.
Van An, L. (2022) Generalized Approximation Hyers-Ulam-Rassias Type Stability of Generalized Homomorphisms in Quasi-Banach Algebras Asia. Mathematika, 6, 7-19. https://www.asiamath.org
Krishna, S.V. and Sarma, K.K.M. (1994) Separation of Fuzzy Normed Linear Spaces. Fuzzy Sets and Systems, 63, 207-217. https://doi.org/10.1016/0165-0114(94)90351-4
Mihet, D. and Radu, V. (2008) On the Stability of the Additive Cauchy Functional Equation in Random Normed Spaces. Journal of Mathematical Analysis and Applications, 343, 567-572. https://doi.org/10.1016/j.jmaa.2008.01.100
Mirzavaziri, M. and Moslehian, M.S. (2006) A Fixed Point Approach to Stability of a Quadratic Equation. Bulletin of the Brazilian Mathematical Society, 37, 361-376.
https://doi.org/10.1007/s00574-006-0016-z
Mohammadi, M., Cho, Y.J., Park, C., Vetro, P. and Saadati, R. (2010) Random Stability of an Additive-Quadratic-Quartic Functional Equation. Journal of Inequalities and Applications, 2010, Article ID: 754210. https://doi.org/10.1155/2010/754210
Najati, A. and Cho, Y.J. (2011) Generalized Hyers-Ulam Stability of the Pexiderized Cauchy Functional Equation in Non-Archimedean Spaces. Fixed Point Theory and Applications, 2011, Article ID: 309026. https://doi.org/10.1155/2011/309026
Najati, A., Kang, J.I. and Cho, Y.J. (2011) Local Stability of the Pexiderized Cauchy and Jensen’s Equations in Fuzzy Spaces. Journal of Inequalities and Applications, 2011, Article No. 78. https://doi.org/10.1186/1029-242X-2011-78
Park, C. (2007) Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras. Fixed Point Theory and Applications, 2007, Article ID: 50175. https://doi.org/10.1155/2007/50175
Park, C. (2008) Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations: A Fixed Point Approach. Fixed Point Theory and Applications, 2008, Article ID: 493751. https://doi.org/10.1155/2008/493751
Rassias, Th.M. (1978) On the Stability of the Linear Mapping in Banach Spaces. Proceedings of the AMS, 72, 297-300.
https://doi.org/10.1090/S0002-9939-1978-0507327-1
Saadati, R. and Park, C. (2010) Non-Archimedean L-Fuzzy Normed Spaces and Stability of Functional Equations. Computers & Mathematics with Applications, 60, 2488-2496. https://doi.org/10.1016/j.camwa.2010.08.055
Skof, F. (1983) Proprieta locali e approssimazione di operatori. Rendiconti del Seminario Matematico e Fisico di Milano, 53, 113-129.
https://doi.org/10.1007/BF02924890
Diaz, J. and Margolis, B. (1968) A Fixed Point Theorem of the Alternative for Contractions on a Generalized Complete Metric Space. Bulletin of the AMS, 74, 305-309. https://doi.org/10.1090/S0002-9904-1968-11933-0