Approximate bi-homomorphisms and bi-derivations in $C^*$-ternary algebras
Bull. Korean Math. Soc. 2010 Vol. 47, No. 1, 195-209
https://doi.org/10.4134/BKMS.2010.47.1.195
Printed January 1, 2010
Jae-Hyeong Bae and Won-Gil Park
Kyung Hee University and National Institute for Mathematical Sciences
Abstract : In this paper, we prove the generalized Hyers-Ulam stability of bi-homomorphisms in $C^*$-ternary algebras and of bi-derivations on $C^*$-ternary algebras for the following bi-additive functional equation $$f(x+y,z-w)+f(x-y,z+w)=2f(x,z)-2f(y,w).$$ This is applied to investigate bi-isomorphisms between $C^*$-ternary algebras.
Keywords : bi-additive mapping, $C^*$-ternary algebra
MSC numbers : Primary 39B82, 46B03, 47Jxx
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