Proper CQ∗ -ternary algebras

In this paper, modifying the construction of a C∗-ternary algebra from a given C∗-algebra, we define a proper CQ∗-ternary algebra from a given proper CQ∗-algebra. We investigate homomorphisms in proper CQ∗-ternary algebras and derivations on proper CQ∗-ternary algebras associated with the Cauchy functional inequality ‖f(x) + f(y) + f(z)‖ ≤ ‖f(x+ y + z)‖. We moreover prove the Hyers-Ulam stability of homomorphisms in proper CQ∗-ternary algebras and of derivations on proper CQ∗-ternary algebras associated with the Cauchy functional equation f(x+ y + z) = f(x) + f(y) + f(z). c ©2014 All rights reserved.