Stability of Functional Equations in C ∗-Ternary Algebras

Yeol Je Cho, Choonkil Park, Themistocles M. Rassias and Reza Saadati
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Yeol Je Cho: Gyeongsang National University College of Education, Department of Mathematics Education and the RINS
Choonkil Park: Hanyang University, Department of Mathematics
Themistocles M. Rassias: National Technical University of Athens, Department of Mathematics
Reza Saadati: Iran University of Science and Technology, Department of Mathematics

Chapter Chapter 5 in Stability of Functional Equations in Banach Algebras, 2015, pp 201-228 from Springer

Abstract: Abstract Ternary algebraic operations were considered in the nineteenth century by several mathematicians such as Cayley (Am J Math 4:1–15, 1881) who introduced the notion of cubic matrix which, in turn, was generalized by Kapranov et al. (Discriminants, resultants and multidimensional determinants. Birkhäuser, Berlin, 1994). The simplest example of such non-trivial ternary operation is given by the following composition rule: { a , b , c } i j k = ∑ 1 ≤ l , m , n ≤ N a n i l b l j m c m k n $$\displaystyle{\{a,b,c\}_{ijk} =\sum _{1\leq l,m,n\leq N}a_{nil}b_{ljm}c_{mkn}}$$ for each i , j , k = 1 , 2 , ⋯ , N $$i,j,k = 1,2,\cdots \,,N$$ .

Keywords: Quadratic Functional Equation; Kapranov; Multidimensional Determinants; Hyers Ulam Stability; Fixed Point Method (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-18708-2_5

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