AbstractAssume that $$\Omega \subset \mathbb {R}^k$$
Ω
⊂
R
k
is an open set, V is a real separable Banach space and $$f_1,\ldots ,f_N :\Omega \rightarrow \Omega $$
f
1
,
…
,
f
N
:
Ω
→
Ω
, $$g_1,\ldots , g_N:\Omega \rightarrow \mathbb {R}$$
g
1
,
…
,
g
N
:
Ω
→
R
, $$h_0:\Omega \rightarrow V$$
h
0
:
Ω
→
V
are given functions. We are interested in the existence and uniqueness of solutions $$\varphi :\Omega \rightarrow V$$
φ
:
Ω
→
V
of the linear equation $$\varphi =\sum _{k=1}^{N}g_k\cdot (\varphi \circ f_k)+h_0$$
φ
=
∑
k
=
1
N
g
k
·
(
φ
∘
f
k
)
+
h
0
in generalized Orlicz spaces.