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Stability problems for generalized additive mappings and Euler-Lagrange type mappings. (English) Zbl 1245.39020
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)].

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
47H10 Fixed-point theorems
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