Todoroki, M.; Kumahara, K.; Miura, T.; Takahasi, S.-E. Stability problems for generalized additive mappings and Euler-Lagrange type mappings. (English) Zbl 1245.39020 Aust. J. Math. Anal. Appl. 9, No. 1, Article No. 19, 9 p. (2012). Summary: We introduce a generalized additivity of a mapping between Banach spaces and establish the Ulam type stability problem for a generalized additive mapping. The obtained results are somewhat different from the Ulam type stability result of Euler-Lagrange type mappings obtained by H.-M. Kim, K.-W. Jun and J. M. Rassias [JIPAM, J. Inequal. Pure Appl. Math. 8, No. 4, Paper No. 120, 17 p., electronic only (2007; Zbl 1141.39028)]. Cited in 1 Document MSC: 39B82 Stability, separation, extension, and related topics for functional equations 47H10 Fixed-point theorems Keywords:Hyers-Ulam stability; Euler-Lagrange functional equation; Banach fixed point theorem PDF BibTeX XML Cite \textit{M. Todoroki} et al., Aust. J. Math. Anal. Appl. 9, No. 1, Article No. 19, 9 p. (2012; Zbl 1245.39020) Full Text: Link