The stability of N-dimensional quadratic functional inequality in non Archimedean Banach spaces
In this paper, using the direct method, we study the stability of the following inequality: f ∑ i = 1 n x i + ∑ 1 ≤ i ≺ j ≤ n f ( x i - x j ) - n ∑ i = 1 n f ( x i ) ≤ f ∑ i = 1 n x i n + ∑ 1 ≤ i ≺ j ≤ n f x i - x j n - 1 n ∑ i = 1 n f ( x i ) in Banach spaces, and the stability of the following ine...
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| Veröffentlicht in: | São Paulo Journal of Mathematical Sciences 2022-12, Vol.16 (2), p.1382-1400 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, using the direct method, we study the stability of the following inequality:
f
∑
i
=
1
n
x
i
+
∑
1
≤
i
≺
j
≤
n
f
(
x
i
-
x
j
)
-
n
∑
i
=
1
n
f
(
x
i
)
≤
f
∑
i
=
1
n
x
i
n
+
∑
1
≤
i
≺
j
≤
n
f
x
i
-
x
j
n
-
1
n
∑
i
=
1
n
f
(
x
i
)
in Banach spaces, and the stability of the following inequality:
f
∑
i
=
1
n
x
i
n
+
∑
1
≤
i
≺
j
≤
n
f
x
i
-
x
j
n
-
1
n
∑
i
=
1
n
f
(
x
i
)
∗
≤
f
∑
i
=
1
n
x
i
+
∑
1
≤
i
≺
j
≤
n
f
(
x
i
-
x
j
)
-
n
∑
i
=
1
n
f
(
x
i
)
∗
,
in non-Archimedean Banach spaces with
n
an integer greater than or equal to 2. |
|---|---|
| ISSN: | 1982-6907 2316-9028 2306-9028 |
| DOI: | 10.1007/s40863-021-00220-9 |