• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.291-305
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• 2018

In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.247-254
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation f(x + ky) - k²f(x + y) + 2(k² - 1)f(x) - k²f(x - y) + f(x - ky) - k²(k² - 1)(f(y) + f(-y)) = 0, where k is a fixed real number with |k| ≠ 0, 1.