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On approximate $$C^*$$-ternary $$m$$-homomorphisms: a fixed point approach. (English) Zbl 1216.39036
Summary: Using fixed point methods, we prove the stability and superstability of $$C^{\ast}$$-ternary additive, quadratic, cubic, and quartic homomorphisms in $$C^{\ast}$$-ternary rings for the functional equation $$f(2x + y) + f(2x - y) + (m - 1) (m-2) (m-3) f(y) = 2^{m - 2} [f (x + y) + f(x - y) + 6f(x)]$$, for each $$m = 1,2,3,4$$.

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges
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