Affiliation:
1. School of Science, University of Phayao , Phayao 56000 , Thailand
2. Research Institute for Convergence of Basic Sciences, Hanyang University , Seoul 04763 , Korea
Abstract
Abstract
In this study, we solve the system of additive functional equations:
h
(
x
+
y
)
=
h
(
x
)
+
h
(
y
)
,
g
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
,
2
f
x
+
y
2
=
g
(
x
)
+
g
(
y
)
,
\left\{\begin{array}{l}h\left(x+y)=h\left(x)+h(y),\\ g\left(x+y)=f\left(x)+f(y),\\ 2f\left(\frac{x+y}{2}\right)=g\left(x)+g(y),\end{array}\right.
and we investigate the stability of (homomorphism, derivation)-systems in Banach algebras.