On approximate ternary m-derivations and σ-homomorphisms

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• 作者：A. G. Ghazanfari ; Z. Alizadeh
• 关键词：Primary 39B82 ; 39B72 ; Secondary 39B52 ; 46H25 ; Ternary algebras ; stability ; approximation ; derivations ; homomorphisms
• 刊名：Journal of Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：17
• 期：4
• 页码：625-640
• 全文大小：644 KB
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  31.Park C., Ras
• 作者单位：A. G. Ghazanfari (1)
  Z. Alizadeh (1)
  
  1. Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Iran
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Mathematical Methods in Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1661-7746

文摘

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