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

Abstract

In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras.

Cubic derivations on Banach algebras

“…Taking the limit as n tend to infinity in (12) and applying (14), we can see that the inequality (10) holds. Now, replacing a, b by 2 n a, 2 n b, respectively in (8), we get…”

“…M. Rassias [16]. Subsequently, the stability problems of various functional equation have been extensively investigated by a number of authors (for example, [2], [12] and [14]). In particular, one of the functional equations which has been studied frequently is the cubic functional equation:…”

A Fixed Point Approach to the Stability of Quartic Lie ∗-Derivations

“…In fact, the stability problems have been extensively investigated to the various points of views such as various functional equations, various spaces and so on. Especially, Jang and Park [9] introduced the concepts of * -derivations and investigated the stability problems of quadratic * -derivations on Banach C * -algebra. Also, Park and Bodaghi and Yang et al studied the stability properties of * -derivations by using an alternative fixed point method; see [12] and [19].…”

Approximate Generalized Cubic*-Derivations

“…By using fixed point methods the stability problems of several functional equations have been extensively investigated by a number of authors; see [6][7][8][9]. Also, Jang and Park [10] investigated the stability of * -derivations and of quadratic * -derivations with Cauchy functional equation and the Jensen functional equation on Banach * -algebra. In particular, the stability of * -derivations on Banach * -algebra by using fixed point alternative was proved by Park and Bodaghi; see [11].…”