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Generalized stability of Euler-Lagrange quadratic functional equation. (English) Zbl 1246.39026
Summary: The main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability theorem of the following Euler-Lagrange type quadratic functional equation $f(ax + by) + af(x - by) = (a + 1)b^2 f(y) + a(a + 1)f(x)$, in $(\beta, p)$-Banach space, where $a, b$ are fixed rational numbers such that $a \neq - 1, 0$ and $b \neq 0$.
39B82Stability, separation, extension, and related topics
Full Text: DOI
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