Approximation of additive functional equations in NA Lie C*-algebras

Abstract

In this paper, by using fixed point method, we approximate a stable map of higher *-derivation in NA C*-algebras and of Lie higher *-derivations in NA Lie C*-algebras associated with the following additive functional equation,where m ≥ 2.

$C^{*}$-Algebra valued fuzzy normed spaces with application of Hyers–Ulam stability of a random integral equation

“…A complete C * AVFN-space is called a C * -algebra valued fuzzy Banach space (in short, a C * AVFB-space). Recently, some authors discussed the approximation of functional equations in several spaces by using a direct technique and a fixed point technique; for fuzzy Menger normed algebras, see [24]; for fuzzy metric spaces, see [25,26]; for FN spaces, see [27]; for non-Archimedean random Lie C * -algebras, see [28]; for non-Archimedean random normed spaces, see [29]; for random multi-normed space, see [30]; and we also refer the reader to [31][32][33][34].…”

Approximation of derivations and the superstability in random Banach ∗-algebras

“…For more details, see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Definition 2.4 A random Banach * -algebra B is a random complex Banach algebra (B, μ, T, T ), together with an involution on B which is a mapping g → g * from B into B that satisfies (i) g * * = g for g ∈ B;…”