Approximate bi-homomorphisms and bi-derivations in $C^*$-ternary algebras

Jae-Hyeong Bae; Won-Gil Park

doi:10.4134/BKMS.2010.47.1.195

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2010; 47(1): 195-209

Printed January 1, 2010

https://doi.org/10.4134/BKMS.2010.47.1.195

Approximate bi-homomorphisms and bi-derivations in $C^*$-ternary algebras

Jae-Hyeong Bae and Won-Gil Park

Kyung Hee University and National Institute for Mathematical Sciences

Abstract

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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