Generalized ulam-hyers stability of C*-Ternary algebra n-Homomorphisms for a functional equation

Park, Won-Gil; Bae, Jae-Hyeong

doi:10.1186/1029-242x-2011-30

Cited by 2 publications

(2 citation statements)

References 21 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The important area of research of ternary structures (cf. [19]) are ternary algebras, ternary linear algebras, normed ternary linear algebras, involutive ternary linear algebras, topological ternary linear algebras, C * -ternary algebras, and Banach ternary algebras (see [20][21][22][23][24][25][26]). Furthermore, the ternary algebraic structures and the n-ary algebraic structures are considered in the theory of functional equations (see [27][28][29][30]).…”

Section: Introductionmentioning

confidence: 99%

Ternary Menger Algebras: A Generalization of Ternary Semigroups

Nongmanee

Leeratanavalee

2021

Mathematics

View full text Add to dashboard Cite

Let n be a fixed natural number. Menger algebras of rank n, which was introduced by Menger, K., can be regarded as the suitable generalization of arbitrary semigroups. Based on this knowledge, an interesting question arises: what a generalization of ternary semigroups is. In this article, we first introduce the notion of ternary Menger algebras of rank n, which is a canonical generalization of arbitrary ternary semigroups, and discuss their related properties. In the second part, we establish the so-called a diagonal ternary semigroup which its operation is induced by the operation on ternary Menger algebras of rank n and then investigate their interesting properties. Moreover, we introduce the concept of homomorphism and congruences on ternary Menger algebras of rank n. These lead us to study the quotient ternary Menger algebras of rank n and to investigate the homomorphism theorem for ternary Menger algebra of rank n with respect to congruences. Furthermore, the characterization of reduction of ternary Menger algebra into Menger algebra is presented.

show abstract

Section: Introductionmentioning

confidence: 99%

Ternary Menger Algebras: A Generalization of Ternary Semigroups

Nongmanee

Leeratanavalee

2021

Mathematics

View full text Add to dashboard Cite

show abstract

“…Theorem 4.2. Let r < 1 and θ be positive real numbers, and let f : A → A be a mapping satisfying (22), (23) and f (0) = 0. Then there exists a unique C * -ternary derivation δ : A → A such that…”

mentioning

confidence: 99%

Jordan derivations on $C^*$-ternary algebras for a Cauchy-Jensen functional equation

Park,

Rassias,

Park

2011

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Generalized ulam-hyers stability of C*-Ternary algebra n-Homomorphisms for a functional equation

Abstract: In this article, we investigate the Ulam-Hyers stability of C*-ternary algebra nhomomorphisms for the functional equation:

Cited by 2 publications

References 21 publications

Ternary Menger Algebras: A Generalization of Ternary Semigroups

Ternary Menger Algebras: A Generalization of Ternary Semigroups

Jordan derivations on $C^*$-ternary algebras for a Cauchy-Jensen functional equation

Contact Info

Product

Resources

About