ALMOST QUADRATIC LIE *-DERIVATIONS ON CONVEX MODULAR *-ALGEBRAS

Abstract

In this article, we investigate an approximate quadratic Lie *-derivation of a quadratic functional equation

f(ax+by)+abf(x-y)=(a+b)(af(x)+bf(y)),

where ab≠0, a, b ∈ ℕ, associated with the identity f([x, y]) = [f(x), y^{2}] +[x^{2}, f(y)] on a ρ-complete convex modular *-algebra χ_{ρ}by using Δ2-condition via convex modular ρ