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Ulam stability of a quartic functional equation. (English) Zbl 1237.39026
Summary: The oldest quartic functional equation was introduced by {\it J. M. Rassias} [Glas. Mat. 34, No. 2, 243--252 (1999; Zbl 0951.39008)], and then was employed by other authors. The functional equation $f(2x + y) + f(2x - y) = 4f(x + y) + 4f(x - y) + 24f(x) - 6f(y)$ is called a {\it quartic functional equation}, all of its solution is said to be a {\it quartic function}. In the current paper, the Hyers-Ulam stability and the superstability for quartic functional equations are established by using the fixed-point alternative theorem.

MSC:
39B82Stability, separation, extension, and related topics
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References:
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