# Proper $CQ^*$-ternary algebras

Volume 7, Issue 4, pp 278--287
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### Authors

Choonkil Park - Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea.

### Abstract

In this paper, modifying the construction of a $C^*$-ternary algebra from a given $C^*$-algebra, we define a proper $CQ^*$-ternary algebra from a given proper $CQ^*$-algebra. We investigate homomorphisms in proper $CQ^*$-ternary algebras and derivations on proper $CQ^*$-ternary algebras associated with the Cauchy functional inequality $\|f(x) + f(y) + f(z)\| \leq\| f(x + y + z)\|.$ We moreover prove the Hyers-Ulam stability of homomorphisms in proper $CQ^*$-ternary algebras and of derivations on proper $CQ^*$-ternary algebras associated with the Cauchy functional equation $f(x + y + z) = f(x) + f(y) + f(z).$

### Share and Cite

##### ISRP Style

Choonkil Park, Proper $CQ^*$-ternary algebras, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 4, 278--287

##### AMA Style

Park Choonkil, Proper $CQ^*$-ternary algebras. J. Nonlinear Sci. Appl. (2014); 7(4):278--287

##### Chicago/Turabian Style

Park, Choonkil. "Proper $CQ^*$-ternary algebras." Journal of Nonlinear Sciences and Applications, 7, no. 4 (2014): 278--287

### Keywords

• proper $CQ^*$-ternary homomorphism
• proper $CQ^*$-ternary derivation
• Cauchy functional equation
• Hyers-Ulam stability.

•  47B48
•  39B72
•  47J05
•  39B52
•  17A40
•  47L60

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