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On approximate ternary m-derivations and σ-homomorphisms

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Abstract

In this paper, we introduce ternary modules over ternary algebras and, using fixed point methods, we prove the stability and superstability of ternary additive, quadratic, cubic and quartic derivations and σ-homomorphisms in such structures for the functional equation

$$\begin{array}{ll} f(ax\,+\,y)\,+\,f(ax\,-\,y)\\ \quad =\,a^{m-2}[f(x\,+\,y)\,+\,f(x\,-\,y)]\\ \qquad +\,2(a^{2}\,-\,1)\big[a^{m-2}f(x)\,+\,\frac{(m\,-\,2)(1\,-\,(m\,-\,2)^{2})}{6}\,f(y)\big]\end{array}$$

for each m = 1, 2, 3, 4.

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Ghazanfari, A.G., Alizadeh, Z. On approximate ternary m-derivations and σ-homomorphisms. J. Fixed Point Theory Appl. 17, 625–640 (2015). https://doi.org/10.1007/s11784-015-0250-3

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