Approximate Cubic ∗‐Derivations on Banach ∗‐Algebras

Abstract

We study the stability of cubic ∗-derivations on Banach ∗-algebras. We also prove the superstability of cubic ∗-derivations on a Banach ∗-algebraA, which is left approximately unital.

Two multi-cubic functional equations and some results on the stability in modular spaces

“…found its general solution, and studied the Hyers-Ulam stability problem for it [18]. For other forms of the (generalized) cubic functional equations and their stability on the various Banach spaces, we refer to [3-7, 29, 35, 36], and [49]. Recently, the stability of multicubic and multi-quartic mappings in Banach spaces via the fixed point method were investigated in [9] and [8], respectively.…”

The General Solution and Approximations of a Decic Type Functional Equation in Various Normed Spaces

“…The fixed point method was used for the first time by Baker [9] who applied a variant of Banachs fixed point theorem to obtain the Hyers-Ulam stability of a functional equation in a single variable (for more applications of this method, see [5,6,13,14,15,16,42,66]). During the last seven decades, the stability problems of various functional equations in several spaces such as intuitionistic fuzzy normed spaces, random normed spaces, non-Archimedean fuzzy normed spaces, Banach spaces, orthogonal spaces and many spaces have been broadly investigated by number of mathematicians; for instance, see [7,10,11,18,21,24,25,27,28,35,39,40,49,50,53,54,55,69].…”