Sentence examples for ternary semigroup from inspiring English sources
In Section 2, we define ternary γ-homomorphism on ternary semigroup and investigate their relations.
We say that is a ternary semigroup if the operation is associative, that is, if holds for all (see [2]).
In this paper, we introduce the notions of γ-homomorphism and γ-derivation of a ternary semigroup and investigate γ-homomorphism and γ-derivations on ternary semigroup associated with the following functional in-equality |f([xyz]) - f(x) - f y) - f z)| ≤ φ x, y, z) and |f([xxx]) - 3f(x)| ≤ φ x, x, x), respectively.
A ternary semigroup (G, ) is a ternary group if for all a, b, c ∈ G, there are x, y, z ∈ G such that [ x a b ] = [ a y b ] = [ a b z ] = c.
In next section, firstly we define ternary γ-derivation on ternary semigroup and investigate ternary γ-derivations on ternary semigroups with the following functional inequality |f([xxx]) - 3f(x)| ≤ φ x, x, x).
Let G be a commutative ternary semigroup and φ : G × G × G → [0, ∞) be a function such that φ ̃ ( x, y, z ) : = 1 3 ∑ n = 0 ∞ 3 - n φ ( x 3 n, y 3 n, z 3 n ) < ∞. Suppose that H G → → G and f : G → [0, ∞) are functions satisfying (2) and (3).
In this section, we introduce concept ternary (γ, h -derivations on ternary semigroups and investigate ternary (γ, h -derivations on ternary semigroups with the following functionandinvestigate|f([xxx]) - 3f(x)| < φ(x, x, x).
In this article, using a sequence of Hyers type, we prove the generalized Hyers-Ulam-Rassias stability of ternary γ-homomorphisms and ternary γ-derivations on commutative ternary semigroups.
In the first section, which have preliminary character, we review some basic definitions and properties related to ternary groups and semigroups (cf. also Rusakov [16]).
