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).