ternary algebras
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2021 ◽  
Vol 65 (1) ◽  
pp. 25-58
Author(s):  
Sylvain Attan ◽  
◽  
Donatien Gaparayi ◽  
Keyword(s):  

Hom-hyporeductive triple algebras are defined as a twisted generalization of hyporeductive triple algebras. Hom-hyporeductive triple algebras generalize right Hom-Lie-Yamaguti and right Hom-Bol algebras as the same way as hyporeductive triple algebras generalize right Lie-Yamaguti and right Bol algebras. It is shown that the category of Hom-hyporeductive triple algebras is closed under the process of taking nth derived binary-ternary Hom-algebras and by self-morphisms of binary-ternary algebras. Some examples of Hom-hyporeductive triple algebras are given.


2020 ◽  
Vol 36 (9) ◽  
pp. 1025-1038
Author(s):  
Yuan Feng Jin ◽  
Choonkil Park ◽  
Michael Th. Rassias
Keyword(s):  

2020 ◽  
Vol 125 (1) ◽  
pp. 79-86
Author(s):  
Pradchaya Piajan ◽  
Rukchart Prasertpong
Keyword(s):  

2019 ◽  
Vol 43 (2) ◽  
pp. 199-215
Author(s):  
Utsanee Leerawat ◽  
Pradchaya Piajan
Keyword(s):  

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1439-1445
Author(s):  
M. Rabbani ◽  
M. Eshaghi

In this article, weintroduce a kind of binary relation on a nonempty set with name of orthogonally relation which we develop for sequences, continuous maps, metric spaces, contraction maps, preserving maps and etc. All of the above concepts are generalized forms of ordinary case, so they are very important for extension and finding new results. we expect some of the concepts in the mathematics can be changed by orthogonally relation, such as functional equations and some of the theorem in the fixed point theorem method. In this research we illustrate one of the applications of orthogonally relation on ternary cubic homomorphism and ternary cubic derivations, so we prove the stability of orthogonally ternary cubic homomorphisms and orthogonally ternary cubic derivations on C*-ternary algebras for the functional equation by using fixed point method. Also to create the stability, we choose a suitable control function and we show ability and validity of the proposed method for the functional analysis.


2015 ◽  
Vol 11 (3) ◽  
pp. 3114-3120
Author(s):  
Soo Hwan Kim

In this paper, we prove the generalized Hyers-Ulam stability of $\sigma$-homomorphisms and derivations on $C^*$-ternary algebras associated with the generalized Cauchy-Jensen type additive functional equation\begin{equation*}\sum_{i=1}^n f\left(x_i +{1 \over n-1}\sum_{j=1, j \ne i}^n x_j\right) =2 \sum_{i=1}^n f(x_i) \end{equation*}where $n \in \Z^+$ is a fixed integers with $n \ge 2$.


2015 ◽  
Vol 22 (4) ◽  
pp. 383-387
Author(s):  
EON WHA SHIM ◽  
MADJID ESHAGHI GORDJI ◽  
JUNG RYE LEE

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