Existence of a solution of integral equations via fixed point theorem
In this paper, we establish a solution to the following integral equation: 1 u ( t ) = ∫ 0 T G ( t , s ) f ( s , u ( s ) ) d s for all t ∈ [ 0 , T ] , where T > 0 , f : [ 0 , T ] × R → R and G : [ 0 , T ] × [ 0 , T ] → [ 0 , ∞ ) are continuous functions. For this purpose, we also obtain some aux...
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| Veröffentlicht in: | Journal of inequalities and applications 2013-11, Vol.2013 (1), Article 529 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we establish a solution to the following integral equation:
1
u
(
t
)
=
∫
0
T
G
(
t
,
s
)
f
(
s
,
u
(
s
)
)
d
s
for all
t
∈
[
0
,
T
]
,
where
T
>
0
,
f
:
[
0
,
T
]
×
R
→
R
and
G
:
[
0
,
T
]
×
[
0
,
T
]
→
[
0
,
∞
)
are continuous functions. For this purpose, we also obtain some auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature.
MSC:
47H10, 54H25. |
|---|---|
| ISSN: | 1029-242X 1029-242X |
| DOI: | 10.1186/1029-242X-2013-529 |