Approximate Additive Functional Equations in Closed Convex Cone

Abstract

In this paper, we introduce the following positive-additive
functional equation in C*-algebras
f

x + 4 4
p
x3y + 6
p
xy + 4 4
p
xy3 + y

=
f(x) + 4f(x)
34
4 p
f(y) + 6
p
f(x)f(y) + 4f(y)
3
4 4
p
f(x) + f(y).
Using the fixed point method, we prove the stability of the positiveadditive
functional equation in C-algebras. Moreover, we prove the
Hyers-Ulam stability of the above functional equation in C-algebras
by the direct method of Hyers-Ulam.