Chang, Ick-Soon Higher ring derivation and intuitionistic fuzzy stability. (English) Zbl 1251.39019 Abstr. Appl. Anal. 2012, Article ID 503671, 16 p. (2012). Summary: We take account of the stability of higher ring derivation in intuitionistic fuzzy Banach algebra associated to the Jensen type functional equation. In addition, we deal with the superstability of higher ring derivation in intuitionistic fuzzy Banach algebra with unit. Cited in 2 Documents MSC: 39B82 Stability, separation, extension, and related topics for functional equations 46S40 Fuzzy functional analysis 46L57 Derivations, dissipations and positive semigroups in \(C^*\)-algebras 39B52 Functional equations for functions with more general domains and/or ranges Keywords:stability; higher ring derivation; intuitionistic fuzzy Banach algebra; Jensen type functional equation PDF BibTeX XML Cite \textit{I.-S. Chang}, Abstr. Appl. Anal. 2012, Article ID 503671, 16 p. (2012; Zbl 1251.39019) Full Text: DOI References: [1] S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York, NY, USA, 1960. · Zbl 0086.24101 [2] D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 27, pp. 222-224, 1941. · Zbl 0061.26403 [3] T. Aoki, “On the stability of the linear transformation in Banach spaces,” Journal of the Mathematical Society of Japan, vol. 2, pp. 64-66, 1950. · Zbl 0040.35501 [4] T. M. Rassias, “On the stability of the linear mapping in Banach spaces,” Proceedings of the American Mathematical Society, vol. 72, no. 2, pp. 297-300, 1978. · Zbl 0398.47040 [5] Y.-S. Jung and I.-S. Chang, “On approximately higher ring derivations,” Journal of Mathematical Analysis and Applications, vol. 343, no. 2, pp. 636-643, 2008. · Zbl 1144.39024 [6] R. Saadati, Y. J. Cho, and J. Vahidi, “The stability of the quartic functional equation in various spaces,” Computers & Mathematics with Applications, vol. 60, no. 7, pp. 1994-2002, 2010. · Zbl 1205.39029 [7] R. Saadati and C. Park, “Non-Archimedian L-fuzzy normed spaces and stability of functional equations,” Computers & Mathematics with Applications, vol. 60, no. 8, pp. 2488-2496, 2010. · Zbl 1205.39023 [8] R. Badora, “On approximate ring homomorphisms,” Journal of Mathematical Analysis and Applications, vol. 276, no. 2, pp. 589-597, 2002. · Zbl 1014.39020 [9] D. G. Bourgin, “Approximately isometric and multiplicative transformations on continuous function rings,” Duke Mathematical Journal, vol. 16, pp. 385-397, 1949. · Zbl 0033.37702 [10] R. Badora, “On approximate derivations,” Mathematical Inequalities & Applications, vol. 9, no. 1, pp. 167-173, 2006. · Zbl 1093.39024 [11] A. K. Mirmostafaee and M. S. Moslehian, “Fuzzy almost quadratic functions,” Results in Mathematics, vol. 52, no. 1-2, pp. 161-177, 2008. · Zbl 1157.46048 [12] A. K. Mirmostafaee and M. S. Moslehian, “Fuzzy versions of Hyers-Ulam-Rassias theorem,” Fuzzy Sets and Systems, vol. 159, no. 6, pp. 720-729, 2008. · Zbl 1178.46075 [13] S. A. Mohiuddine, “Stability of Jensen functional equation in intuitionistic fuzzy normed space,” Chaos, Solitons & Fractals, vol. 42, no. 5, pp. 2989-2996, 2009. · Zbl 1198.39034 [14] S. A. Mohiuddine, M. Cancan, and H. \cSevli, “Intuitionistic fuzzy stability of a Jensen functional equation via fixed point technique,” Mathematical and Computer Modelling, vol. 54, no. 9-10, pp. 2403-2409, 2011. · Zbl 1235.39027 [15] M. Mursaleen and S. A. Mohiuddine, “On stability of a cubic functional equation in intuitionistic fuzzy normed spaces,” Chaos, Solitons & Fractals, vol. 42, no. 5, pp. 2997-3005, 2009. · Zbl 1198.39035 [16] R. Saadati and J. H. Park, “On the intuitionistic fuzzy topological spaces,” Chaos, Solitons and Fractals, vol. 27, no. 2, pp. 331-344, 2006. · Zbl 1083.54514 [17] M. Mursaleen, V. Karakaya, and S. A. Mohiuddine, “Schauder basis, separability, and approximation property in intuitionistic fuzzy normed space,” Abstract and Applied Analysis, vol. 2010, Article ID 131868, 14 pages, 2010. · Zbl 1219.46070 [18] M. Mursaleen and S. A. Mohiuddine, “Statistical convergence of double sequences in intuitionistic fuzzy normed spaces,” Chaos, Solitons & Fractals, vol. 41, no. 5, pp. 2414-2421, 2009. · Zbl 1198.40007 [19] M. Mursaleen and S. A. Mohiuddine, “On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space,” Journal of Computational and Applied Mathematics, vol. 233, no. 2, pp. 142-149, 2009. · Zbl 1183.46070 [20] M. Mursaleen, S. A. Mohiuddine, and O. H. H. Edely, “On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 603-611, 2010. · Zbl 1189.40003 [21] B. Dinda, T. K. Samanta, and U. K. Bera, “Intuitionistic fuzzy Banach algebra,” Bulletin of Mathematical Analysis and Applications, vol. 3, no. 3, pp. 273-281, 2011. · Zbl 1314.46087 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.