Newton-type method for solving generalized inclusion View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2021-03-31

AUTHORS

P. S. M. Santos, G. N. Silva, R. C. M. Silva

ABSTRACT

In this paper, we propose and study the problem of solve non-linear inclusion problem in Banach spaces, where the involved operator can be written as sum of a Fréchet differentiable function with a continuous perturbation. We use a specific technique introduced by Robinson (Numer. Math. 19, 341–347, 1972) to obtain Newton-Kantorovich theorem, which extends the results of Rokne (Numer. Math. 18, 401–412, 1971), for instance. In our main convergence result, we assume a kind of Hölder condition. Thus, one of the major difficulties to obtain our main result is to show that the sequence of scalars associated with the Newton sequence is convergent. Numerical examples are given to justify the theoretical results. More... »

PAGES

1811-1829

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11075-021-01096-8

DOI

http://dx.doi.org/10.1007/s11075-021-01096-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1136820100


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Campus Ministro Reis Velloso, Universidade Federal do Delta do Parna\u00edba, Parna\u00edba, PI, Brazil", 
          "id": "http://www.grid.ac/institutes/None", 
          "name": [
            "Campus Ministro Reis Velloso, Universidade Federal do Delta do Parna\u00edba, Parna\u00edba, PI, Brazil"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Santos", 
        "givenName": "P. S. M.", 
        "id": "sg:person.011357167137.28", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011357167137.28"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Centro das Ci\u00eancias Exatas e das Tecnologias, Universidade Federal do Oeste da Bahia, CEP 47808-021, Barreiras, BA, Brazil", 
          "id": "http://www.grid.ac/institutes/grid.472638.c", 
          "name": [
            "Centro das Ci\u00eancias Exatas e das Tecnologias, Universidade Federal do Oeste da Bahia, CEP 47808-021, Barreiras, BA, Brazil"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Silva", 
        "givenName": "G. N.", 
        "id": "sg:person.016672542147.21", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016672542147.21"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Departamento de Matem\u00e1tica, Universidade Federal do Amazonas, Manaus, AM, Brazil", 
          "id": "http://www.grid.ac/institutes/grid.411181.c", 
          "name": [
            "Departamento de Matem\u00e1tica, Universidade Federal do Amazonas, Manaus, AM, Brazil"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Silva", 
        "givenName": "R. C. M.", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s11075-009-9308-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000640161", 
          "https://doi.org/10.1007/s11075-009-9308-x"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01406677", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019497520", 
          "https://doi.org/10.1007/bf01406677"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-0-387-87821-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022362018", 
          "https://doi.org/10.1007/978-0-387-87821-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s40314-018-0617-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1103172740", 
          "https://doi.org/10.1007/s40314-018-0617-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01436488", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052532345", 
          "https://doi.org/10.1007/bf01436488"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01385696", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045998532", 
          "https://doi.org/10.1007/bf01385696"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10589-007-9082-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053719030", 
          "https://doi.org/10.1007/s10589-007-9082-4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01404880", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048822194", 
          "https://doi.org/10.1007/bf01404880"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10440-017-0146-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1095857321", 
          "https://doi.org/10.1007/s10440-017-0146-x"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2021-03-31", 
    "datePublishedReg": "2021-03-31", 
    "description": "In this paper, we propose and study the problem of solve non-linear inclusion problem in Banach spaces, where the involved operator can be written as sum of a Fr\u00e9chet differentiable function with a continuous perturbation. We use a specific technique introduced by Robinson (Numer. Math. 19, 341\u2013347, 1972) to obtain Newton-Kantorovich theorem, which extends the results of Rokne (Numer. Math. 18, 401\u2013412, 1971), for instance. In our main convergence result, we assume a kind of H\u00f6lder condition. Thus, one of the major difficulties to obtain our main result is to show that the sequence of scalars associated with the Newton sequence is convergent. Numerical examples are given to justify the theoretical results.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s11075-021-01096-8", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1050467", 
        "issn": [
          "1017-1398", 
          "1572-9265"
        ], 
        "name": "Numerical Algorithms", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "4", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "88"
      }
    ], 
    "keywords": [
      "main convergence result", 
      "Newton\u2013Kantorovich theorem", 
      "Newton-type method", 
      "Fr\u00e9chet differentiable function", 
      "Newton sequence", 
      "convergence results", 
      "Banach spaces", 
      "sequence of scalars", 
      "numerical examples", 
      "continuous perturbations", 
      "differentiable functions", 
      "H\u00f6lder condition", 
      "theoretical results", 
      "involved operators", 
      "inclusion problem", 
      "main results", 
      "theorem", 
      "major difficulty", 
      "problem", 
      "scalar", 
      "operators", 
      "perturbations", 
      "space", 
      "convergent", 
      "sum", 
      "results", 
      "function", 
      "Robinson", 
      "instances", 
      "Rokne", 
      "technique", 
      "specific techniques", 
      "kind", 
      "sequence", 
      "conditions", 
      "difficulties", 
      "inclusion", 
      "example", 
      "paper", 
      "method"
    ], 
    "name": "Newton-type method for solving generalized inclusion", 
    "pagination": "1811-1829", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1136820100"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s11075-021-01096-8"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s11075-021-01096-8", 
      "https://app.dimensions.ai/details/publication/pub.1136820100"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-05-10T10:30", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220509/entities/gbq_results/article/article_884.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s11075-021-01096-8"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s11075-021-01096-8'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s11075-021-01096-8'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11075-021-01096-8'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11075-021-01096-8'


 

This table displays all metadata directly associated to this object as RDF triples.

153 TRIPLES      22 PREDICATES      74 URIs      57 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s11075-021-01096-8 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N3ed6bee0e0d7432c8bd969f3687af8b3
4 schema:citation sg:pub.10.1007/978-0-387-87821-8
5 sg:pub.10.1007/bf01385696
6 sg:pub.10.1007/bf01404880
7 sg:pub.10.1007/bf01406677
8 sg:pub.10.1007/bf01436488
9 sg:pub.10.1007/s10440-017-0146-x
10 sg:pub.10.1007/s10589-007-9082-4
11 sg:pub.10.1007/s11075-009-9308-x
12 sg:pub.10.1007/s40314-018-0617-3
13 schema:datePublished 2021-03-31
14 schema:datePublishedReg 2021-03-31
15 schema:description In this paper, we propose and study the problem of solve non-linear inclusion problem in Banach spaces, where the involved operator can be written as sum of a Fréchet differentiable function with a continuous perturbation. We use a specific technique introduced by Robinson (Numer. Math. 19, 341–347, 1972) to obtain Newton-Kantorovich theorem, which extends the results of Rokne (Numer. Math. 18, 401–412, 1971), for instance. In our main convergence result, we assume a kind of Hölder condition. Thus, one of the major difficulties to obtain our main result is to show that the sequence of scalars associated with the Newton sequence is convergent. Numerical examples are given to justify the theoretical results.
16 schema:genre article
17 schema:inLanguage en
18 schema:isAccessibleForFree false
19 schema:isPartOf N8ed2e8de2bd54882a2982be11ff547da
20 Na52be9f6a1eb477da2aefec891169459
21 sg:journal.1050467
22 schema:keywords Banach spaces
23 Fréchet differentiable function
24 Hölder condition
25 Newton sequence
26 Newton-type method
27 Newton–Kantorovich theorem
28 Robinson
29 Rokne
30 conditions
31 continuous perturbations
32 convergence results
33 convergent
34 differentiable functions
35 difficulties
36 example
37 function
38 inclusion
39 inclusion problem
40 instances
41 involved operators
42 kind
43 main convergence result
44 main results
45 major difficulty
46 method
47 numerical examples
48 operators
49 paper
50 perturbations
51 problem
52 results
53 scalar
54 sequence
55 sequence of scalars
56 space
57 specific techniques
58 sum
59 technique
60 theorem
61 theoretical results
62 schema:name Newton-type method for solving generalized inclusion
63 schema:pagination 1811-1829
64 schema:productId Na98712ebf6d04b76a96d2b91989e100c
65 Nb21cdebab361438b849e3a9258323e55
66 schema:sameAs https://app.dimensions.ai/details/publication/pub.1136820100
67 https://doi.org/10.1007/s11075-021-01096-8
68 schema:sdDatePublished 2022-05-10T10:30
69 schema:sdLicense https://scigraph.springernature.com/explorer/license/
70 schema:sdPublisher N02b257e4c9664c32add0420b7bbcfc6a
71 schema:url https://doi.org/10.1007/s11075-021-01096-8
72 sgo:license sg:explorer/license/
73 sgo:sdDataset articles
74 rdf:type schema:ScholarlyArticle
75 N02b257e4c9664c32add0420b7bbcfc6a schema:name Springer Nature - SN SciGraph project
76 rdf:type schema:Organization
77 N399d4e7115b1426889d9749807248329 rdf:first sg:person.016672542147.21
78 rdf:rest Ne2deab137ad942a3a68fcbb57a1e3a94
79 N3ed6bee0e0d7432c8bd969f3687af8b3 rdf:first sg:person.011357167137.28
80 rdf:rest N399d4e7115b1426889d9749807248329
81 N52c9c49477c64ac5b35c62fbb82279dc schema:affiliation grid-institutes:grid.411181.c
82 schema:familyName Silva
83 schema:givenName R. C. M.
84 rdf:type schema:Person
85 N8ed2e8de2bd54882a2982be11ff547da schema:issueNumber 4
86 rdf:type schema:PublicationIssue
87 Na52be9f6a1eb477da2aefec891169459 schema:volumeNumber 88
88 rdf:type schema:PublicationVolume
89 Na98712ebf6d04b76a96d2b91989e100c schema:name dimensions_id
90 schema:value pub.1136820100
91 rdf:type schema:PropertyValue
92 Nb21cdebab361438b849e3a9258323e55 schema:name doi
93 schema:value 10.1007/s11075-021-01096-8
94 rdf:type schema:PropertyValue
95 Ne2deab137ad942a3a68fcbb57a1e3a94 rdf:first N52c9c49477c64ac5b35c62fbb82279dc
96 rdf:rest rdf:nil
97 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
98 schema:name Mathematical Sciences
99 rdf:type schema:DefinedTerm
100 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
101 schema:name Pure Mathematics
102 rdf:type schema:DefinedTerm
103 sg:journal.1050467 schema:issn 1017-1398
104 1572-9265
105 schema:name Numerical Algorithms
106 schema:publisher Springer Nature
107 rdf:type schema:Periodical
108 sg:person.011357167137.28 schema:affiliation grid-institutes:None
109 schema:familyName Santos
110 schema:givenName P. S. M.
111 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011357167137.28
112 rdf:type schema:Person
113 sg:person.016672542147.21 schema:affiliation grid-institutes:grid.472638.c
114 schema:familyName Silva
115 schema:givenName G. N.
116 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016672542147.21
117 rdf:type schema:Person
118 sg:pub.10.1007/978-0-387-87821-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022362018
119 https://doi.org/10.1007/978-0-387-87821-8
120 rdf:type schema:CreativeWork
121 sg:pub.10.1007/bf01385696 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045998532
122 https://doi.org/10.1007/bf01385696
123 rdf:type schema:CreativeWork
124 sg:pub.10.1007/bf01404880 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048822194
125 https://doi.org/10.1007/bf01404880
126 rdf:type schema:CreativeWork
127 sg:pub.10.1007/bf01406677 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019497520
128 https://doi.org/10.1007/bf01406677
129 rdf:type schema:CreativeWork
130 sg:pub.10.1007/bf01436488 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052532345
131 https://doi.org/10.1007/bf01436488
132 rdf:type schema:CreativeWork
133 sg:pub.10.1007/s10440-017-0146-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1095857321
134 https://doi.org/10.1007/s10440-017-0146-x
135 rdf:type schema:CreativeWork
136 sg:pub.10.1007/s10589-007-9082-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053719030
137 https://doi.org/10.1007/s10589-007-9082-4
138 rdf:type schema:CreativeWork
139 sg:pub.10.1007/s11075-009-9308-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1000640161
140 https://doi.org/10.1007/s11075-009-9308-x
141 rdf:type schema:CreativeWork
142 sg:pub.10.1007/s40314-018-0617-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1103172740
143 https://doi.org/10.1007/s40314-018-0617-3
144 rdf:type schema:CreativeWork
145 grid-institutes:None schema:alternateName Campus Ministro Reis Velloso, Universidade Federal do Delta do Parnaíba, Parnaíba, PI, Brazil
146 schema:name Campus Ministro Reis Velloso, Universidade Federal do Delta do Parnaíba, Parnaíba, PI, Brazil
147 rdf:type schema:Organization
148 grid-institutes:grid.411181.c schema:alternateName Departamento de Matemática, Universidade Federal do Amazonas, Manaus, AM, Brazil
149 schema:name Departamento de Matemática, Universidade Federal do Amazonas, Manaus, AM, Brazil
150 rdf:type schema:Organization
151 grid-institutes:grid.472638.c schema:alternateName Centro das Ciências Exatas e das Tecnologias, Universidade Federal do Oeste da Bahia, CEP 47808-021, Barreiras, BA, Brazil
152 schema:name Centro das Ciências Exatas e das Tecnologias, Universidade Federal do Oeste da Bahia, CEP 47808-021, Barreiras, BA, Brazil
153 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...