Convergence to common fixed points by a modified iteration process View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2010-01-29

AUTHORS

Safeer Hussain Khan, Y. J. Cho, Mujahid Abbas

ABSTRACT

We modify an iteration process of Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61–79, 2007) to the case of two mappings and prove some weak and strong convergence theorems for two asymptotically nonexpansive mappings. We also point out that this process cannot be used for three mappings in its existing form even for nonexpansive mappings. We have to impose an extra condition to get convergence. We give an example to show that there do exist two nonexpansive mappings satisfying that condition. More... »

PAGES

607-616

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s12190-010-0381-z

DOI

http://dx.doi.org/10.1007/s12190-010-0381-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1016099312


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/2008/08", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Information and Computing Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, Statistics and Physics, Qatar University, 2713, Doha, Qatar", 
          "id": "http://www.grid.ac/institutes/grid.412603.2", 
          "name": [
            "Department of Mathematics, Statistics and Physics, Qatar University, 2713, Doha, Qatar"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Khan", 
        "givenName": "Safeer Hussain", 
        "id": "sg:person.010266761613.61", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010266761613.61"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics Education, Gyeongsang National University, Chinju, South Korea", 
          "id": "http://www.grid.ac/institutes/grid.256681.e", 
          "name": [
            "Department of Mathematics Education, Gyeongsang National University, Chinju, South Korea"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Cho", 
        "givenName": "Y. J.", 
        "id": "sg:person.07455740051.00", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07455740051.00"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, Lahore University of Management Sciences, 54792, Lahore, Pakistan", 
          "id": "http://www.grid.ac/institutes/grid.440540.1", 
          "name": [
            "Department of Mathematics, Lahore University of Management Sciences, 54792, Lahore, Pakistan"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Abbas", 
        "givenName": "Mujahid", 
        "id": "sg:person.014160432337.79", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014160432337.79"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2010-01-29", 
    "datePublishedReg": "2010-01-29", 
    "description": "We modify an iteration process of Agarwal et al. (J.\u00a0Nonlinear Convex Anal. 8(1):61\u201379, 2007) to the case of two mappings and prove some weak and strong convergence theorems for two asymptotically nonexpansive mappings. We also point out that this process cannot be used for three mappings in its existing form even for nonexpansive mappings. We have to impose an extra condition to get convergence. We give an example to show that there do exist two nonexpansive mappings satisfying that condition.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s12190-010-0381-z", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136398", 
        "issn": [
          "1598-5865", 
          "1865-2085"
        ], 
        "name": "Journal of Applied Mathematics and Computing", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1-2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "35"
      }
    ], 
    "keywords": [
      "cases", 
      "iteration process", 
      "process", 
      "Agarwal", 
      "al", 
      "mapping", 
      "strong convergence theorems", 
      "convergence theorem", 
      "theorem", 
      "nonexpansive mappings", 
      "form", 
      "extra conditions", 
      "conditions", 
      "convergence", 
      "example", 
      "point", 
      "modified iteration process"
    ], 
    "name": "Convergence to common fixed points by a modified iteration process", 
    "pagination": "607-616", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1016099312"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s12190-010-0381-z"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s12190-010-0381-z", 
      "https://app.dimensions.ai/details/publication/pub.1016099312"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2021-12-01T19:23", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20211201/entities/gbq_results/article/article_516.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s12190-010-0381-z"
  }
]
 

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/s12190-010-0381-z'

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/s12190-010-0381-z'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s12190-010-0381-z'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s12190-010-0381-z'


 

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

95 TRIPLES      21 PREDICATES      42 URIs      34 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s12190-010-0381-z schema:about anzsrc-for:01
2 anzsrc-for:08
3 schema:author N92e657cdb94745819dbc8a8344a5e985
4 schema:datePublished 2010-01-29
5 schema:datePublishedReg 2010-01-29
6 schema:description We modify an iteration process of Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61–79, 2007) to the case of two mappings and prove some weak and strong convergence theorems for two asymptotically nonexpansive mappings. We also point out that this process cannot be used for three mappings in its existing form even for nonexpansive mappings. We have to impose an extra condition to get convergence. We give an example to show that there do exist two nonexpansive mappings satisfying that condition.
7 schema:genre article
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf N0381051a7c1b4d3fa0460b96cf9bdc53
11 N2aa87f1d104a4de1b83a2c082454662b
12 sg:journal.1136398
13 schema:keywords Agarwal
14 al
15 cases
16 conditions
17 convergence
18 convergence theorem
19 example
20 extra conditions
21 form
22 iteration process
23 mapping
24 modified iteration process
25 nonexpansive mappings
26 point
27 process
28 strong convergence theorems
29 theorem
30 schema:name Convergence to common fixed points by a modified iteration process
31 schema:pagination 607-616
32 schema:productId N230b9d9b9cc04ef281b4994017927397
33 N7fe2835721b24e069bca1964ec98182e
34 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016099312
35 https://doi.org/10.1007/s12190-010-0381-z
36 schema:sdDatePublished 2021-12-01T19:23
37 schema:sdLicense https://scigraph.springernature.com/explorer/license/
38 schema:sdPublisher Nb269f111850745289ec82680389ab26b
39 schema:url https://doi.org/10.1007/s12190-010-0381-z
40 sgo:license sg:explorer/license/
41 sgo:sdDataset articles
42 rdf:type schema:ScholarlyArticle
43 N0381051a7c1b4d3fa0460b96cf9bdc53 schema:volumeNumber 35
44 rdf:type schema:PublicationVolume
45 N230b9d9b9cc04ef281b4994017927397 schema:name doi
46 schema:value 10.1007/s12190-010-0381-z
47 rdf:type schema:PropertyValue
48 N2aa87f1d104a4de1b83a2c082454662b schema:issueNumber 1-2
49 rdf:type schema:PublicationIssue
50 N7fe2835721b24e069bca1964ec98182e schema:name dimensions_id
51 schema:value pub.1016099312
52 rdf:type schema:PropertyValue
53 N92e657cdb94745819dbc8a8344a5e985 rdf:first sg:person.010266761613.61
54 rdf:rest N990c103e86d64be280d1a40cc88b9f4a
55 N990c103e86d64be280d1a40cc88b9f4a rdf:first sg:person.07455740051.00
56 rdf:rest Nc65c4fa74736420288fd9562d731f0b9
57 Nb269f111850745289ec82680389ab26b schema:name Springer Nature - SN SciGraph project
58 rdf:type schema:Organization
59 Nc65c4fa74736420288fd9562d731f0b9 rdf:first sg:person.014160432337.79
60 rdf:rest rdf:nil
61 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
62 schema:name Mathematical Sciences
63 rdf:type schema:DefinedTerm
64 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
65 schema:name Information and Computing Sciences
66 rdf:type schema:DefinedTerm
67 sg:journal.1136398 schema:issn 1598-5865
68 1865-2085
69 schema:name Journal of Applied Mathematics and Computing
70 schema:publisher Springer Nature
71 rdf:type schema:Periodical
72 sg:person.010266761613.61 schema:affiliation grid-institutes:grid.412603.2
73 schema:familyName Khan
74 schema:givenName Safeer Hussain
75 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010266761613.61
76 rdf:type schema:Person
77 sg:person.014160432337.79 schema:affiliation grid-institutes:grid.440540.1
78 schema:familyName Abbas
79 schema:givenName Mujahid
80 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014160432337.79
81 rdf:type schema:Person
82 sg:person.07455740051.00 schema:affiliation grid-institutes:grid.256681.e
83 schema:familyName Cho
84 schema:givenName Y. J.
85 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07455740051.00
86 rdf:type schema:Person
87 grid-institutes:grid.256681.e schema:alternateName Department of Mathematics Education, Gyeongsang National University, Chinju, South Korea
88 schema:name Department of Mathematics Education, Gyeongsang National University, Chinju, South Korea
89 rdf:type schema:Organization
90 grid-institutes:grid.412603.2 schema:alternateName Department of Mathematics, Statistics and Physics, Qatar University, 2713, Doha, Qatar
91 schema:name Department of Mathematics, Statistics and Physics, Qatar University, 2713, Doha, Qatar
92 rdf:type schema:Organization
93 grid-institutes:grid.440540.1 schema:alternateName Department of Mathematics, Lahore University of Management Sciences, 54792, Lahore, Pakistan
94 schema:name Department of Mathematics, Lahore University of Management Sciences, 54792, Lahore, Pakistan
95 rdf:type schema:Organization
 




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


...