The aim of this paper is to show that under some mild conditions a functional equation of multiplicative (a, b)-derivation is superstable on standard operator algebras. Furthermore, we prove that this generalized derivation can be a continuous and an inner (a, b)- derivation.

In this paper, we will consider Hyers-Ulam-Rassias stability of multipliers and ring derivations between Banach algebras. As a corollary, we will prove super stability of ring derivations and multipliers. That is, approximate multipliers and approximate ring derivations are exact multipliers and ring derivations.

In this paper, we solve and investigate the superstability of the $p$-radical functional equations related to the following Wilson and Kim functional equations \begin{align*}f\left(\sqrt[p]{x^{p}+y^{p}}\right) &+f\left(\sqrt[p]{x^{p}-y^{p}}\right)=\lambda f(x) g(y),\\f\left(\sqrt[p]{x^{p}+y^{p}}\right) &+f\left(\sqrt[p]{x^{p}-y^{p}}\right)=\lambda g(x) f(y),\end{align*}where $p$ is an odd positive integer and $f$ is a complex valued function. Furthermore, the results are extended to Banach algebras.

In this paper, first, we introduce the new concept of 2-inner product on Banach modules over a C-algebra. Next, we present the concept of 2-linear operators over a C-algebra. Our result improve the main result of the paper [Z. Lewandowska, On 2-normed sets, Glasnik Mat., 38(58) (2003), 99-110]. In the end of this paper, we define the notions 2-adjointable mappings between 2-pre Hilbert C*-modules and prove superstability of them in the spirit of Hyers-Ulam-Rassias.

In this paper some results about the Hyers-Ulam-Rassias stability for the linear functional equations in general form and its Pexiderized can be proved for given functions on general domain to a complex Banach spaces under some suitable conditions. In connection with the problem of G. L. Forti in the 13st ICFEI we consider the common stability for the systems of functional equations and our aim is to establish some common Hyers-Ulam-Rassias stability for systems of homogeneous linear functional equations. The results is applied to the study of some superstability results for the exponential functional equation.