On the Stability of Additive, Quadratic, Cubic and Quartic Set-valued Functional Equations
For m = 1, 2, 3, 4, we study the following set-valued functional equation f ( a x + y ) ⊕ f ( a x - y ) = a m - 2 [ f ( x + y ) ⊕ f ( x - y ) ] ⊕ 2 ( a 2 - 1 ) [ a m - 2 f ( x ) ⊕ ( m - 2 ) ( 1 - ( m - 2 ) 2 ) 6 f ( y ) ] where a is a fixed positive integer with a > 1. We also prove the stabili...
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| Veröffentlicht in: | Resultate der Mathematik 2015-09, Vol.68 (1-2), p.1-10 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | For
m
= 1, 2, 3, 4, we study the following set-valued functional equation
f
(
a
x
+
y
)
⊕
f
(
a
x
-
y
)
=
a
m
-
2
[
f
(
x
+
y
)
⊕
f
(
x
-
y
)
]
⊕
2
(
a
2
-
1
)
[
a
m
-
2
f
(
x
)
⊕
(
m
-
2
)
(
1
-
(
m
-
2
)
2
)
6
f
(
y
)
]
where
a
is a fixed positive integer with
a
> 1. We also prove the stability of this set-valued functional equation by using the Banach fixed point theorem. |
|---|---|
| ISSN: | 1422-6383 1420-9012 |
| DOI: | 10.1007/s00025-014-0416-0 |