Generalized Hyers–Ulam stability of ρ-functional inequalities
In our research work generalized Hyers-Ulam stability of the following functional inequalities is analyzed by using fixed point approach: 0.1 ∥ f ( 2 x + y ) + f ( 2 x − y ) − 2 f ( x + y ) − 2 f ( x − y ) − 12 f ( x ) − ρ ( 4 f ( x + y 2 ) + 4 ( f ( x − y 2 ) − f ( x + y ) − f ( x − y ) ) − 6 f ( x...
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| Published in | Journal of inequalities and applications Vol. 2023; no. 1; pp. 135 - 18 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
24.10.2023
Springer Nature B.V SpringerOpen |
| Subjects | |
| Online Access | Get full text |
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| Summary: | In our research work generalized Hyers-Ulam stability of the following functional inequalities is analyzed by using fixed point approach:
0.1
∥
f
(
2
x
+
y
)
+
f
(
2
x
−
y
)
−
2
f
(
x
+
y
)
−
2
f
(
x
−
y
)
−
12
f
(
x
)
−
ρ
(
4
f
(
x
+
y
2
)
+
4
(
f
(
x
−
y
2
)
−
f
(
x
+
y
)
−
f
(
x
−
y
)
)
−
6
f
(
x
)
,
r
)
∥
≥
r
r
+
φ
(
x
,
y
)
and
0.2
∥
f
(
2
x
+
y
)
+
f
(
2
x
−
y
)
−
4
f
(
x
+
y
)
−
4
f
(
x
−
y
)
−
24
f
(
x
)
+
6
f
(
y
)
−
ρ
(
8
f
(
x
+
y
2
)
+
8
(
f
(
x
−
y
2
)
−
2
f
(
x
+
y
)
−
2
f
(
x
−
y
)
)
−
12
f
(
x
)
+
3
f
(
y
)
,
r
)
∥
≥
r
r
+
φ
(
x
,
y
)
in the setting of fuzzy matrix, where
ρ
≠
2
is a real number.
We also discussed Hyers-Ulam stability from the application point of view. |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1029-242X 1025-5834 1029-242X |
| DOI: | 10.1186/s13660-023-03047-4 |