Approximately Partial Ternary Quadratic Derivations on Banach Ternary Algebras

Abstract

Abstract. Let A 1 , A 2 , ..., A n be normed ternary algebras over the complex field C and let B be a Banach ternary algebra over C. A mapping δ k from A 1 × · · · × A n into B is called a k-th partial ternary quadratic derivation if there exists a mapping g k : A k

Nearly k-th Partial Ternary Quadratic *-Derivations

“…Recently, Javadian and et al [10] established the Hyers-Ulam-Rassias stability of the partial ternary quadratic derivations in Banach ternary algebras by using the direct method.…”

“…. , A n be normed ternary algebras over the complex field C and let B be a Banach ternary algebra over C. As in [10], a mapping δ k :…”

Approximate *-derivations and approximate quadratic *-derivations on C*-algebras

“…A generalized version of the theorem of Hyers for an approximately linear mapping was given by Rassias [7]. Since then, the stability problems of various functional equations have been extensively investigated by a number of authors (see [8][9][10][11][12][13][14][15][16][17][18][19]). In particular, those of the important functional equations are the following functional equations…”

“…Moreover, it follows from (2.5) with m = 0 and (2.6) that δ(a) − f (a) ≤φ(a, a, 0, 0) for all a ∈ A. It is well known that the additive mapping δ satisfying (2.4) is unique (see [3] or [19]). Replacing a and a* by 2 n a and 2 n a*, respectively, in (2.3), we get…”