Strong convergence of an inertial Halpern type algorithm in Banach spaces
In this article, we obtain the strong convergence of the new modified Halpern iteration process x n + 1 = α n u + ( 1 - α n ) T n P ( x n + θ n ( x n - x n - 1 ) ) , n = 1 , 2 , 3 , … , to a common fixed point of { T n } , where { T n } n = 1 ∞ is a family of nonexpansive mappings on the closed and...
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| Vydáno v: | Rendiconti del Circolo matematico di Palermo Ročník 72; číslo 2; s. 1517 - 1526 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cham
Springer International Publishing
01.03.2023
|
| Témata: | |
| ISSN: | 0009-725X, 1973-4409 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | In this article, we obtain the strong convergence of the new modified Halpern iteration process
x
n
+
1
=
α
n
u
+
(
1
-
α
n
)
T
n
P
(
x
n
+
θ
n
(
x
n
-
x
n
-
1
)
)
,
n
=
1
,
2
,
3
,
…
,
to a common fixed point of
{
T
n
}
, where
{
T
n
}
n
=
1
∞
is a family of nonexpansive mappings on the closed and convex subset
C
of a Banach space
X
,
P
:
X
⟶
C
is a nonexpansive retraction,
{
α
n
}
⊂
[
0
,
1
]
and
{
θ
n
}
⊂
R
+
. Some applications of this result are also presented. |
|---|---|
| ISSN: | 0009-725X 1973-4409 |
| DOI: | 10.1007/s12215-022-00749-4 |