Abstract
AbstractLet X, Y be real normed spaces and let $$\rho '_+$$
ρ
+
′
, $$\rho '_-$$
ρ
-
′
be norm derivatives. In this work, we solve a system of functional equations $$\begin{aligned} {\left\{ \begin{array}{ll}\rho '_+(f(x),f(y))=g(x)\rho '_+(x,y),\\ \rho '_-(f(x),f(y))=g(x)\rho '_-(x,y), \end{array}\right. } \end{aligned}$$
ρ
+
′
(
f
(
x
)
,
f
(
y
)
)
=
g
(
x
)
ρ
+
′
(
x
,
y
)
,
ρ
-
′
(
f
(
x
)
,
f
(
y
)
)
=
g
(
x
)
ρ
-
′
(
x
,
y
)
,
with unknown functions $$f:X\!\rightarrow \!Y$$
f
:
X
→
Y
, $$g:X\rightarrow \mathbb {R}$$
g
:
X
→
R
. Moreover, we give partial answer to open problem posed in 2010.
Publisher
Springer Science and Business Media LLC
Subject
Control and Optimization,Analysis,Algebra and Number Theory
Reference14 articles.
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