C*-Ternary Biderivations and C*-Ternary Bihomomorphisms

Abstract

Abstract:In this paper, we investigate C * -ternary biderivations and C * -ternary bihomomorphism in C * -ternary algebras, associated with bi-additive s-functional inequalities.

Hyers-Ulam-Rassias Stability of the $C^*$-ternary Bi-homomorphisms and $C^*$-ternary Bi-derivations in $C^*$-ternary Algebras

“…• If we take ϕ(x, y, z, w) = θ x r + y r + z r + w r for all x, y, z, w ∈ A, then we get that (i) If r < 2, then Theorem 2.1 recover Theorem 1 in [16] with the Lipschitz L = 2 r−2 . (ii) If r > 6, then Theorem 2.2 recover Theorem 2 in [16] with the Lipschitz L = 2 6−r .…”

“…This implies that (1.2) is also meaningless. Next, Park [16] corrected the above definition as follows Definition 1.2. Let A and B be C * -ternary algebras.…”

“…Moreover, Park [16] proved the Hyers-Ulam stability of C * -ternary bi-homomorphisms and C * -ternary bi-derivations in C * -ternary algebras and investigated the stability results of C *ternary bi-homomorphisms and C * -ternary bi-derivations in C * -ternary algebras associated with the following bi-additive s-functional inequalities…”