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Ulam stability of hom-ders in fuzzy Banach algebras

  • Received: 11 May 2022 Revised: 28 June 2022 Accepted: 05 July 2022 Published: 08 July 2022
  • MSC : 47H10, 39B82

  • This paper aims to investigate a new type of derivations in a fuzzy Banach algebra. Moreover, by using the fixed point method, we obtain some stability results of the hom-der in fuzzy Banach algebras associated with the functional equation

    $ f(x+{\textbf{k}}y) = f(x)+{\textbf{k}}f(y) $

    where $ {\textbf{k}} $ is a fixed positive integer greater than $ 1 $.

    Citation: Araya Kheawborisut, Siriluk Paokanta, Jedsada Senasukh, Choonkil Park. Ulam stability of hom-ders in fuzzy Banach algebras[J]. AIMS Mathematics, 2022, 7(9): 16556-16568. doi: 10.3934/math.2022907

    Related Papers:

  • This paper aims to investigate a new type of derivations in a fuzzy Banach algebra. Moreover, by using the fixed point method, we obtain some stability results of the hom-der in fuzzy Banach algebras associated with the functional equation

    $ f(x+{\textbf{k}}y) = f(x)+{\textbf{k}}f(y) $

    where $ {\textbf{k}} $ is a fixed positive integer greater than $ 1 $.



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    [1] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64–66. http://dx.doi.org/10.2969/jmsj/00210064 doi: 10.2969/jmsj/00210064
    [2] T. Bag, S. K. Samanta, Finite dimensional fuzzy normed linear spaces J. Fuzzy Math., 11 (2003), 687–705.
    [3] T. Bînzar, F. Pater, S. Nǎdǎban, On fuzzy normed algebras, J. Nonlinear Sci. Appl., 9 (2016), 5488–5496. http://dx.doi.org/10.22436/jnsa.009.09.16 doi: 10.22436/jnsa.009.09.16
    [4] L. Cǎdariu, V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math., 4 (2003), 4.
    [5] L. Cǎdariu, V. Radu, On the stability of the Cauchy functional equation: A fixed point approach, Grazer Math. Ber., 346 (2004), 43–52.
    [6] Y. Cho, C. Park, Y. Yang, Stability of derivations in fuzzy normed algebras, J. Nonlinear Sci. Appl., 8 (2015), 1–7. http://dx.doi.org/10.22436/jnsa.008.01.01 doi: 10.22436/jnsa.008.01.01
    [7] J. Diaz, B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Am. Math. Soc., 74 (1968), 305–309. http://dx.doi.org/10.1090/S0002-9904-1968-11933-0 doi: 10.1090/S0002-9904-1968-11933-0
    [8] P. Gǎvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431–436. http://dx.doi.org/10.1006/jmaa.1994.1211 doi: 10.1006/jmaa.1994.1211
    [9] Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci., 14 (1991), 817959. http://dx.doi.org/10.1155/S016117129100056X doi: 10.1155/S016117129100056X
    [10] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci., 27 (1941), 222–224. http://dx.doi.org/10.1073/pnas.27.4.222 doi: 10.1073/pnas.27.4.222
    [11] M. Isar, G. Lu, Y. Jin, C. Park, A general additive functional inequality and derivation in Banach algebras, J. Math. Inequal., 15 (2021), 305–321. http://dx.doi.org/10.7153/jmi-2021-15-23 doi: 10.7153/jmi-2021-15-23
    [12] Y. Lee, S. Jung, M. T. Rassias, Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation, J. Math. Inequal., 12 (2018), 43–61. http://dx.doi.org/10.7153/jmi-2018-12-04 doi: 10.7153/jmi-2018-12-04
    [13] M. Mirzavaziri, M. S. Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc., 37 (2006), 361–376. http://dx.doi.org/10.1007/s00574-006-0016-z doi: 10.1007/s00574-006-0016-z
    [14] A. K. Mirmostafaee, M. Mirzavaziri, M. S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets Syst., 159 (2008), 730–738. http://dx.doi.org/10.1016/j.fss.2007.07.011 doi: 10.1016/j.fss.2007.07.011
    [15] A. K. Mirmostafaee, M. S. Moslehian, Fuzzy approximately cubic mappings, Inf. Sci., 178 (2008), 3791–3798. https://doi.org/10.1016/j.ins.2008.05.032 doi: 10.1016/j.ins.2008.05.032
    [16] A. K. Mirmostafaee, Perturbation of generalized derivations in fuzzy Menger normed algebras, Fuzzy Sets Syst., 195 (2012), 109–117. http://dx.doi.org/10.1016/j.fss.2011.10.015 doi: 10.1016/j.fss.2011.10.015
    [17] S. Nǎdǎban, I. Dzitac, Atomic decompositions of fuzzy normed linear spaces for wavelet applications, Informatica, 25 (2014), 643–662. https://doi.org/10.15388/Informatica.2014.33 doi: 10.15388/Informatica.2014.33
    [18] B. Noori, M. B. Moghimi, B. Khosravi, C. Park, Stability of some functional equations on bounded domains, J. Math. Inequal., 14 (2020), 455–472. http://dx.doi.org/10.7153/jmi-2020-14-29 doi: 10.7153/jmi-2020-14-29
    [19] C. Park, Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras, Fixed Point Theory Appl., 2007 (2007), 50175. http://dx.doi.org/10.1155/2007/50175 doi: 10.1155/2007/50175
    [20] C. Park, Generalized Hyers-Ulam-Rassias stability of quadratic functional equations: A fixed point approach, Fixed Point Theory Appl., 2008 (2008), 493751. http://dx.doi.org/10.1155/2008/493751 doi: 10.1155/2008/493751
    [21] C. Park, Homomorphisms between Poisson $JC^{\ast}$-algebras, Bull. Braz. Math. Soc. (N.S.), 36 (2005), 79–97. http://dx.doi.org/10.1007/s00574-005-0029-z doi: 10.1007/s00574-005-0029-z
    [22] V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory, 4 (2003), 91–96.
    [23] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc., 72 (1978), 297–300. http://dx.doi.org/10.1090/S0002-9939-1978-0507327-1 doi: 10.1090/S0002-9939-1978-0507327-1
    [24] R. Saadati, C. Park, Non-Archimedean $\mathcal{L}$-fuzzy normed spaces and stability of functional equations, Comput. Math. Appl., 60 (2010), 2488–2496. http://dx.doi.org/10.1016/j.camwa.2010.08.055 doi: 10.1016/j.camwa.2010.08.055
    [25] M. Sarfraz, Y. Li, Minimum functional equation and some Pexider-type functional equation on any group, AIMS Math., 6 (2021), 11305–11317. http://dx.doi.org/10.3934/math.2021656 doi: 10.3934/math.2021656
    [26] Z. Wang, Approximate mixed type quadratic-cubic functional equation, AIMS Math., 6 (2021), 3546–3561. http://dx.doi.org/10.3934/math.2021211 doi: 10.3934/math.2021211
    [27] S. M. Ulam, A collection of the mathematical problems, Interscience, New York, 1960.
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