×

Approximation of functional equations in intuitionistic fuzzy \(C^\ast\)-algebras. (English) Zbl 1513.39063

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
39B82 Stability, separation, extension, and related topics for functional equations
46S40 Fuzzy functional analysis
Full Text: DOI

References:

[1] S. M. Ulam,A Collection of the Mathematical Problems, Interscience Publ. New York, 1960. · Zbl 0086.24101
[2] D.H. Hyers,On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A.27(1941), 222-224. · JFM 67.0424.01
[3] T. Aoki,On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan2(1950), 64-66. · Zbl 0040.35501
[4] Th.M. Rassias,On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc.72(1978), 297-300. · Zbl 0398.47040
[5] P. Găvruta,A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings,J. Math. Anal. Appl.184(1994), 431-436. · Zbl 0818.46043
[6] J.M. Rassias,On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math.108 (1984), 445-446. · Zbl 0599.47106
[7] J.M. Rassias,On approximation of approximately linear mappings by linear mappings, J. Funct. Anal.46(1982), 126-130. · Zbl 0482.47033
[8] J.M. Rassias,Solution of the Ulam stability problem for quartic mappings, Glas. Mat. Ser.III34 (54)(1999), 243-252. · Zbl 0951.39008
[9] P. Czerwik,Functional Equations and Inequalities in Several Variables, World Scientific Publishing Company, New Jersey, Hong Kong, Singapore and London, 2002. · Zbl 1011.39019
[10] G.L. Forti,Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations, J. Math. Anal. Appl.295(2004), 127-133. · Zbl 1052.39031
[11] G.L. Forti,Elementary remarks on Ulam-Hyers stability of linear functional equations, J. Math. Anal. Appl.328 (2007), 109-118. · Zbl 1111.39026
[12] D.H. Hyers, G. Isac and Th.M. Rassias,Stability of Functional Equations in Several Variables, Birkh¨auser, Basel, 1998. · Zbl 0907.39025
[13] S. Jung,Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press lnc., Palm Harbor, Florida, 2001. · Zbl 0980.39024
[14] L. Cădariu and V. Radu,Fixed points and the stability of Jensen’s functional equation, J. Inequal. Pure Appl. Math.4, no. 1, Art. ID 4 (2003). · Zbl 1043.39010
[15] J. Diaz and B. Margolis,A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc.74(1968), 305-309. · Zbl 0157.29904
[16] R. Saadati, S.M. Vaezpour,Some results on fuzzy Banach spaces, J. Appl. Math. Comput.17(2005), no. 1-2, 475-484. · Zbl 1077.46060
[17] R. Saadati, C. Park,Non-ArchimedianL-fuzzy normed spaces and stability of functional equations,Comput. Math. Appl.60(2010), no. 8, 2488-2496. · Zbl 1205.39023
[18] R.P. Agarwal, Y.J. Cho, R. Saadati, S. Wang,NonlinearL-fuzzy stability of cubic functional equations,J. Inequal. Appl. 2012, 2012:77, 19 pp. · Zbl 1277.39038
[19] R. Saadati,On the “On some results in fuzzy metric spaces”, J. Comput. Anal. Appl.14(2012), no. 6, 996-999. · Zbl 1256.54027
[20] C. Park, S.Y. Jang, R. Saadati,Fuzzy approximate of homomorphisms,J. Comput. Anal. Appl.14(2012), no. 5, 833-841. · Zbl 1269.47042
[21] A.K. Mirmostafaee, M. Mirzavaziri and M.S. Moslehian,Fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems159(2008), 730-738. · Zbl 1179.46060
[22] A.K. Mirmostafaee and M.S. Moslehian,Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets and Systems 159(2008), 720-729. · Zbl 1178.46075
[23] J.I. Kang, R. Saadati,Approximation of homomorphisms and derivations on non-Archimedean random LieC∗algebras via fixed point method, J. Inequal. Appl. 2012, 2012:251, 10 pp. MR3017309 · Zbl 1279.39015
[24] C. Park, M. Eshaghi Gordji, R. Saadati,Random homomorphisms and random derivations in random normed algebras via fixed point method, J. Inequal. Appl. 2012, 2012:194, 13 pp. MR3015424 · Zbl 1310.39020
[25] A. Ebadian, M. Eshaghi Gordji, H. Khodaei, R. Saadati, Gh. Sadeghi,On the stability of anm-variables functional equation in random normed spaces via fixed point method, Discrete Dyn. Nat. Soc. 2012, Art. ID 346561, 13 pp. · Zbl 1244.39022
[26] J.M. Rassias, R. Saadati, Gh. Sadeghi,J. Vahidi,On nonlinear stability in various random normed spaces, J. Inequal. Appl. 2011, 2011:62, 17 pp. MR2837916 · Zbl 1272.39026
[27] Y.J. Cho, R. Saadati,Lattictic non-Archimedean random stability of ACQ functional equation, Adv. Difference Equ. 2011, 2011:31, 12 pp. MR2835985 · Zbl 1273.39024
[28] D. Mihet, R. Saadati,On the stability of the additive Cauchy functional equation in random normed spaces, Appl. Math. Lett.24(2011), no. 12, 2005-2009. · Zbl 1236.39031
[29] C. Park,Lie∗-homomorphisms between LieC∗-algebras and Lie∗-derivations on LieC∗-algebras, J. Math. Anal. Appl.293(2004), 419-434. · Zbl 1051.46052
[30] C. Park,Homomorphisms between LieJ C∗-algebras and Cauchy-Rassias stability of LieJ C∗-algebra derivations, J. Lie Theory15(2005), 393-414. · Zbl 1091.39006
[31] C. Park,Homomorphisms between PoissonJ C∗-algebras, Bull. Braz. Math. Soc.36(2005), 79-97. · Zbl 1091.39007
[32] C. Park, J.R. Lee, Th.M. Rassias, R. Saadati,Fuzzy∗-homomorphisms and fuzzy∗-derivations in induced fuzzy C∗-algebras. Math. Comput. Modelling54(2011), no. 9-10, 2027-2039. · Zbl 1235.46078
[33] J. Vahidi, C. Park, R. Saadati,A functional equation related to inner product spaces in non-ArchimedeanL-random normed spaces. J. Inequal. Appl. 2012, 2012:168, 16 pp. · Zbl 1274.46132
[34] Y.J. Cho, Th.M. Rassias, R. Saadati,Stability of functional equations in random normed spaces. Springer Optimization and Its Applications,86. Springer, New York, 2013. · Zbl 1281.46001
[35] M. Mohamadi, Y.J. Cho, C. Park, P. Vetro, R. Saadati,Random stability on an additive-quadratic-quartic functional equation.J. Inequal. Appl. 2010, Art. ID 754210, 18 pp. · Zbl 1187.39045
[36] J. Dixmier,C∗-Algebras, North-Holland Publ. Com., Amsterdam, New York and Oxford, 1977. · Zbl 0372.46058
[37] K.R. Goodearl,Notes on Real and ComplexC∗-Algebras, Shiva Math. SeriesIV, Shiva Publ. Limited, Cheshire, England, 1982. · Zbl 0495.46039
[38] H.A. Kenary,Hyers-Ulam stability of some functional equations in non-Archimedean and random normed spaces, (preprint). · Zbl 1265.39054
[39] G. Isac and Th.M. Rassias,Stability ofψ-additive mappings: Appications to nonlinear analysis, Internat. J. Math. Math. Sci.19(1996), 219-228. · Zbl 0843.47036
[40] L. Cădariu and V. Radu,On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Ber.346(2004), 43-52. · Zbl 1060.39028
[41] L. Cădariu and V. Radu,Fixed point methods for the generalized stability of functional equations in a single variable, Fixed Point Theory and Applications2008, Art. ID 749392 (2008). · Zbl 1146.39040
[42] M. Mirzavaziri and M.S. Moslehian,A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc.37(2006), 361-376. · Zbl 1118.39015
[43] C. Park,Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras, Fixed Point Theory and Applications2007, Art. ID 50175 (2007). · Zbl 1167.39018
[44] C. Park,Generalized Hyers-Ulam-Rassias stability of quadratic functional equations: a fixed point approach, Fixed Point Theory and Applications2008, Art. ID 493751 (2008). · Zbl 1146.39048
[45] V. Radu,The fixed point alternative and the stability of functional equations, Fixed Point Theory4(2003), 91-96. · Zbl 1051.39031
[46] C. Park, H.A. Kenary, S. Og Kim, Positive-additive functional equations inC∗-algebras. Fixed Point Theory 13 (2012), no. 2, 613-622. · Zbl 1283.39011
[47] D. Miheţ and V. Radu,On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl.343(2008), 567-572. · Zbl 1139.39040
[48] J. H. Park, Intuitionistic fuzzy metric spaces,Chaos, Solitons and Fractals22(2004), 1039-1046. · Zbl 1060.54010
[49] S. B. Hosseini, D. O’Regan and R. Saadati, Some results on intuitionistic fuzzy spaces,Iranian J. Fuzzy Systems, 4(2007), 53-64. · Zbl 1138.54007
[50] R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces,Chaos, Solitons and Fractals27(2006), 331-344. · Zbl 1083.54514
[51] R. Saadati, A note on Some results on the IF-normed spaces,Chaos, Solitons and Fractals41(2009), 206-213. · Zbl 1198.54023
[52] S. Shakeri, Intuitionistic fuzzy stability of Jensen type mapping,J. Nonlinear Sci.2(2009), 105-112 · Zbl 1167.54004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.