2006
DOI: 10.1007/s11005-005-0042-6
|View full text |Cite
|
Sign up to set email alerts
|

Approximate Homomorphisms of Ternary Semigroups

Abstract: In this paper, we prove the generalized Hyers-Ulam-Rassias stability of mappings of commutative semigroups into Banach spaces. In addition, we establish the superstability of ternary homomorphisms into Banach algebras endowed with multiplicative norms.

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
4

Citation Types

0
16
0

Year Published

2010
2010
2022
2022

Publication Types

Select...
5
3

Relationship

0
8

Authors

Journals

citations
Cited by 48 publications
(16 citation statements)
references
References 20 publications
0
16
0
Order By: Relevance
“…Let us recall (see for example [1,2,17]) that a pair (G, [·]), where G is a non-empty set and [·] : G 3 → G is a function (which is said to be a ternary operation), is called a ternary groupoid. Given a mapping ⊕ : G 2 → G, we can define a ternary operation [·] on G by…”
Section: Introductionmentioning
confidence: 99%
See 2 more Smart Citations
“…Let us recall (see for example [1,2,17]) that a pair (G, [·]), where G is a non-empty set and [·] : G 3 → G is a function (which is said to be a ternary operation), is called a ternary groupoid. Given a mapping ⊕ : G 2 → G, we can define a ternary operation [·] on G by…”
Section: Introductionmentioning
confidence: 99%
“…Such ternary algebraic structures appear in various domains of theoretical and mathematical physics (for example "Nambu mechanics" the 4-dimensional Minkowskian space-time, and the algebra of "nonions", which was introduced by Sylvester as a ternary analog of Hamilton's quaternions; see [1,9,13] for details).…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…A C*-ternary algebra is a complex Banach space A, equipped with a ternary product (x, y, z) α [x, y, z] of A 3 into A, which is ℂ-linear in the outer variables, conjugate ℂ- 3 (see [7,8]). Every left Hilbert C*-module is a C*-ternary algebra via the ternary product [x, y, z] := 〈x, y〉 z.…”
Section: Introductionmentioning
confidence: 99%
“…Theorem 3.1. Let p < 2 and θ be positive real numbers, and let f : A×A → A be a mapping satisfying (2) such that…”
mentioning
confidence: 99%