Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces
Let E be a strictly convex real Banach space and let D ⊆ E be a nonempty closed convex subset of E . Let T i : D ⟶ P ( D ) , i = 1 , 2 , 3 , … be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric, P ( D ) is the family of proximinal and...
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| Veröffentlicht in: | Fixed point theory and algorithms for sciences and engineering Jg. 2022; H. 1; S. 1 - 12 |
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| Sprache: | Englisch |
| Veröffentlicht: |
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Springer International Publishing
07.03.2022
SpringerOpen |
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| ISSN: | 2730-5422, 2730-5422 |
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| Abstract | Let
E
be a strictly convex real Banach space and let
D
⊆
E
be a nonempty closed convex subset of
E
. Let
T
i
:
D
⟶
P
(
D
)
,
i
=
1
,
2
,
3
,
…
be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric,
P
(
D
)
is the family of proximinal and bounded subsets of
D
. Supposing that the family has at least one common fixed point, we show that a Krasnoselskii–Mann-type sequence converges strongly to a common fixed point. Our result generalizes and complements some important results for single-valued and multivalued quasinonexpansive maps. |
|---|---|
| AbstractList | Let
E
be a strictly convex real Banach space and let
$D\subseteq E$
D
⊆
E
be a nonempty closed convex subset of
E
. Let
$T_{i}: {D}\longrightarrow \mathcal{P}({D})$
T
i
:
D
⟶
P
(
D
)
,
$i=1,2,3,\ldots $
i
=
1
,
2
,
3
,
…
be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric,
$\mathcal{P}(D)$
P
(
D
)
is the family of proximinal and bounded subsets of
D
. Supposing that the family has at least one common fixed point, we show that a Krasnoselskii–Mann-type sequence converges strongly to a common fixed point. Our result generalizes and complements some important results for single-valued and multivalued quasinonexpansive maps. Let E be a strictly convex real Banach space and let D ⊆ E be a nonempty closed convex subset of E . Let T i : D ⟶ P ( D ) , i = 1 , 2 , 3 , … be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric, P ( D ) is the family of proximinal and bounded subsets of D . Supposing that the family has at least one common fixed point, we show that a Krasnoselskii–Mann-type sequence converges strongly to a common fixed point. Our result generalizes and complements some important results for single-valued and multivalued quasinonexpansive maps. Abstract Let E be a strictly convex real Banach space and let D ⊆ E $D\subseteq E$ be a nonempty closed convex subset of E. Let T i : D ⟶ P ( D ) $T_{i}: {D}\longrightarrow \mathcal{P}({D})$ , i = 1 , 2 , 3 , … $i=1,2,3,\ldots $ be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric, P ( D ) $\mathcal{P}(D)$ is the family of proximinal and bounded subsets of D. Supposing that the family has at least one common fixed point, we show that a Krasnoselskii–Mann-type sequence converges strongly to a common fixed point. Our result generalizes and complements some important results for single-valued and multivalued quasinonexpansive maps. |
| ArticleNumber | 8 |
| Author | Izuazu, Chimezie Minjibir, Ma’aruf Shehu |
| Author_xml | – sequence: 1 givenname: Ma’aruf Shehu orcidid: 0000-0002-1120-6712 surname: Minjibir fullname: Minjibir, Ma’aruf Shehu email: msminjibir.mth@buk.edu.ng organization: African University of Science and Technology, Bayero University – sequence: 2 givenname: Chimezie surname: Izuazu fullname: Izuazu, Chimezie organization: African University of Science and Technology |
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| Cites_doi | 10.2140/pjm.1969.30.475 10.1090/S0002-9947-1970-0257828-6 10.1016/S0362-546X(99)00227-8 10.1155/2013/629468 10.4064/sm-2-1-7-9 10.1007/s13398-017-0382-y 10.1112/jlms/s2-17.3.547 10.1016/j.na.2008.10.112 10.1016/j.na.2011.09.040 10.1090/S0002-9904-1974-13640-2 10.1016/j.na.2020.111958 10.1016/j.jmaa.2013.03.045 10.1088/0266-5611/20/1/006 10.1016/j.jmaa.2013.04.014 10.1090/S0002-9904-1967-11725-7 |
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| Keywords | Strong convergence 47H10 Countable family of maps Multivalued quasinonexpansive maps 47H09 47J25 Stirctly convex Banach space Hausdorff metric |
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| References_xml | – volume: 15 start-page: 257 issue: 2 year: 2014 end-page: 267 ident: CR16 article-title: Iterative algorithm for fixed points of multi-valued pseudo-contractive mappings in Banach spaces publication-title: J. Nonlinear Convex Anal. – volume: 30 start-page: 475 year: 1969 end-page: 488 ident: CR9 article-title: Multivalued contraction mappings publication-title: Pac. J. Math. doi: 10.2140/pjm.1969.30.475 – volume: 149 start-page: 65 year: 1970 end-page: 73 ident: CR3 article-title: On the Mann iterative process publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1970-0257828-6 – volume: 3 start-page: 29 issue: 1 year: 1986 end-page: 35 ident: CR8 article-title: Quasi-nonexpansive mappings and uniform asymptotic regularity publication-title: Kobe J. 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Mon. – volume: 75 start-page: 1895 issue: 4 year: 2012 ident: 718_CR13 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2011.09.040 – volume: 15 start-page: 257 issue: 2 year: 2014 ident: 718_CR16 publication-title: J. Nonlinear Convex Anal. – volume: 59 start-page: 131 year: 1957 ident: 718_CR7 publication-title: Jahresber. Dtsch. Math.-Ver. – volume: 22 start-page: 99 issue: 1 year: 1977 ident: 718_CR11 publication-title: Math. Jpn. – volume: 17 start-page: 547 issue: 2 year: 1978 ident: 718_CR4 publication-title: J. Lond. Math. Soc. doi: 10.1112/jlms/s2-17.3.547 – volume: 30 start-page: 475 year: 1969 ident: 718_CR9 publication-title: Pac. J. Math. doi: 10.2140/pjm.1969.30.475 – volume: 2 start-page: 7 year: 1930 ident: 718_CR23 publication-title: Stud. Math. doi: 10.4064/sm-2-1-7-9 – volume: 149 start-page: 65 year: 1970 ident: 718_CR3 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1970-0257828-6 – volume: 17 start-page: 301 issue: 2 year: 2016 ident: 718_CR20 publication-title: Fixed Point Theory – volume: 43 start-page: 693 year: 2001 ident: 718_CR12 publication-title: Nonlinear Anal. doi: 10.1016/S0362-546X(99)00227-8 – volume: 112 start-page: 373 year: 2018 ident: 718_CR21 publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. doi: 10.1007/s13398-017-0382-y – volume: 2013 year: 2013 ident: 718_CR18 publication-title: Abstr. Appl. Anal. doi: 10.1155/2013/629468 – volume: 2014 year: 2014 ident: 718_CR22 publication-title: Adv. Numer. Anal. |
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| Snippet | Let
E
be a strictly convex real Banach space and let
D
⊆
E
be a nonempty closed convex subset of
E
. Let
T
i
:
D
⟶
P
(
D
)
,
i
=
1
,
2
,
3
,
…
be a countable... Let E be a strictly convex real Banach space and let $D\subseteq E$ D ⊆ E be a nonempty closed convex subset of E . Let $T_{i}: {D}\longrightarrow... Abstract Let E be a strictly convex real Banach space and let D ⊆ E $D\subseteq E$ be a nonempty closed convex subset of E. Let T i : D ⟶ P ( D ) $T_{i}:... |
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| SubjectTerms | Analysis Applications of Mathematics Countable family of maps Differential Geometry Hausdorff metric Mathematical and Computational Biology Mathematics Mathematics and Statistics Multivalued quasinonexpansive maps Stirctly convex Banach space Strong convergence Topology |
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| Title | Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces |
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