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Bull. Korean Math. Soc. 2009; 46(1): 45-60

Printed January 1, 2009

Copyright © The Korean Mathematical Society.

Stability of homomorphisms and derivations in proper $JCQ^{*}$-triples associated to the Pexiderized Cauchy type mapping

Abbas Najati, G. Zamani Eskandani, and Choonkil Park

University of Mohaghegh Ardabili, University of Tabriz, and Hanyang University

Abstract

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In this paper, we investigate homomorphisms in proper $JCQ^{*}$-triples and derivations on proper $JCQ^{*}$-triples associated to the following Pexiderized functional equation \[f(x+y+z) = f_{0} (x)+ f_{1} (y) +f_{2} (z).\] This is applied to investigate homomorphisms and derivations in proper $JCQ^{*}$-triples.

Keywords: generalized Hyers--Ulam stability, proper $JCQ^{*}$-triples homomorphism, proper $JCQ^{*}$-triples derivation

MSC numbers: Primary 39B52, 47N50, 47L60, 47L90, 46H35, 46B03

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