# STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY IN PROPER CQ*-ALGEBRAS

• Lee, Jung-Rye (Department of Mathematics Daejin University) ;
• Park, Choon-Kil (Department of Mathematics Research Institute for Natural Sciences Hanyang University) ;
• Shin, Dong-Yun (Department of Mathematics University of Seoul)
• Published : 2011.07.31

#### Abstract

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

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