Abstract
AbstractIn this paper, we consider the condition $$\sum _{i=0}^{n+1}\varphi _i(r_ix+q_iy)\in {\mathbb {Z}}$$
∑
i
=
0
n
+
1
φ
i
(
r
i
x
+
q
i
y
)
∈
Z
for real valued functions defined on a linear space V. We derive necessary and sufficient conditions for functions satisfying this condition to be decent in the following sense: there exist functions $$f_i:V\rightarrow {\mathbb {R}}$$
f
i
:
V
→
R
, $$g_i:V\rightarrow {\mathbb {Z}}$$
g
i
:
V
→
Z
such that $$\varphi _i=f_i+g_i$$
φ
i
=
f
i
+
g
i
, $$(i=0,\dots ,n+1)$$
(
i
=
0
,
⋯
,
n
+
1
)
and $$\sum _{i=0}^{n+1}f_i(r_ix+q_iy)=0$$
∑
i
=
0
n
+
1
f
i
(
r
i
x
+
q
i
y
)
=
0
for all $$x, y\in V$$
x
,
y
∈
V
.
Funder
EFOP
Hungarian Scientific Research Fund
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,General Mathematics
Reference26 articles.
1. Baker, J.A.: On some mathematical characters. Glas. Mat. Ser. III, 25(45)(2), 319–328 (1990)
2. Baron, K., Forti, G.-L.: Orthogonality and additivity modulo $$\mathbb{Z}$$. Results Math. 26(3–4), 205–210 (1994)
3. Baron, K., Sablik, M., Volkmann, P.: On decent solutions of a functional congruence. Rocznik Nauk. Dydakt. Prace Mat. 17, 27–40 (2000)
4. Baron, K., Volkmann, P.: On the Cauchy equation modulo $$\mathbb{Z}$$. Fundam. Math. 131(2), 143–148 (1988)
5. Borus, G.Gy., Gilányi, A.: On a computer program for solving systems of functional equations. In: 4th IEEE International Conference on Cognitive Infocommunications (CogInfoCom), p. 939. IEEE (2013)
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