Functional Equations in Mathematical Analysis by Themistocles M. M. Rassias & Janusz Brzdek

Author:Themistocles M. M. Rassias & Janusz Brzdek
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

for all x 1 ,…,x n ∈ A, whenever the following conditions hold: (a) (A,⋅) is a group;

(b) a ∈ A is a fixed element;

(c) α ∈Aut (A,⋅), α(a) = a, for any x ∈ A.

28.3 An { n}-arySemigroup of Mappings. The Embedding Theorems

We will consider some n-ary (ternary) semigroups of mappings. The idea and significance of n-ary (ternary) semigroups of mappings will be explained in the problem of representing an n-ary (a ternary) semigroup as an n-ary (a ternary) semigroup of mappings. The main results of this section are the embedding theorems.

Let X and Y be nonempty sets. By T(X, Y ) we denote the set of all mappings of the set X into the set Y.

Assume that X 1, X 2,…,X n − 1, where n ≥ 3, are nonempty sets. Consider the set

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