Fixed point problems for generalized contractions with applications
In this paper, we investigate the conditions on the control mappings ψ , φ : ( 0 , ∞ ) → R that guarantee the existence of the fixed points of the mapping T : X → P ( X ) satisfying the following inequalities: ψ ( H ( T x , T y ) ) ≤ φ ( d ( x , y ) ) ∀ x , y ∈ X , provided that H ( T x , T y ) >...
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| Veröffentlicht in: | Advances in difference equations 2021-05, Vol.2021 (1), p.1-15, Article 247 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we investigate the conditions on the control mappings
ψ
,
φ
:
(
0
,
∞
)
→
R
that guarantee the existence of the fixed points of the mapping
T
:
X
→
P
(
X
)
satisfying the following inequalities:
ψ
(
H
(
T
x
,
T
y
)
)
≤
φ
(
d
(
x
,
y
)
)
∀
x
,
y
∈
X
,
provided that
H
(
T
x
,
T
y
)
>
0
,
and
ψ
(
H
(
T
x
,
T
y
)
)
≤
φ
(
A
(
x
,
y
)
)
∀
x
,
y
∈
X
,
provided that
H
(
T
x
,
T
y
)
>
0
,
where
A
(
x
,
y
)
=
max
{
d
(
x
,
y
)
,
d
(
x
,
T
x
)
,
d
(
y
,
T
y
)
,
(
d
(
x
,
T
y
)
+
d
(
T
x
,
y
)
)
/
2
}
, and
(
X
,
d
)
is a metric space. The obtained fixed point results improve many earlier results on the set-valued contractions. As an application, we consider the existence of the solutions of an FDE. |
|---|---|
| ISSN: | 1687-1847 1687-1839 1687-1847 |
| DOI: | 10.1186/s13662-021-03405-w |