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On the stability of the non-linear Euler-Lagrange functional equation in real normed linear spaces. (English) Zbl 0840.46024

Summary: Ulam imposed the following problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist”. The author [C. R. Acad. Bulg. Sci. 45, No. 6, 17-20 (1992; Zbl 0789.46036)] established an analogous problem for nonlinear Euler-Lagrange mappings. In this paper, we improve our results pertinent to the afore-mentioned stability nonlinear problem in order to hold for larger classes of mappings.

MSC:

46G05 Derivatives of functions in infinite-dimensional spaces
47J05 Equations involving nonlinear operators (general)

Citations:

Zbl 0789.46036
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