Stability of an additive functional inequality in proper $CQ^*$-algebras

Jung Rye Lee; Choonkil Park; Dong Yun Shin

doi:10.4134/BKMS.2011.48.4.853

Bulletin of the
Korean Mathematical Society BKMS

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

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Bull. Korean Math. Soc. 2011; 48(4): 853-871

Printed July 1, 2011

https://doi.org/10.4134/BKMS.2011.48.4.853

Stability of an additive functional inequality in proper $CQ^*$-algebras

Jung Rye Lee, Choonkil Park, and Dong Yun Shin

Daejin University, Hanyang University, University of Seoul

Abstract

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Abstract

In this paper, we prove the Hyers--Ulam--Rassias stability of the following additive functional inequality: \begin{eqnarray} \|f(2x)+f(2y)+2f(z)\| & \le & \|2f(x+y+z)\| . \end{eqnarray} We investigate homomorphisms in proper $CQ^*$-algebras and derivations on proper $CQ^*$-algebras associated with the additive functional inequality {\rm (0.1)}.

Keywords: additive functional inequality, Hyers--Ulam--Rassias stability, proper $CQ^*$-algebras, proper $CQ^*$-algebra homomorphism, derivation

MSC numbers: Primary 39B72; Secondary 47N50, 47L60, 46H35, 47Jxx, 47L90, 46B03