A Picard-Mann hybrid iterative process View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2013-03-25

AUTHORS

Safeer Hussain Khan

ABSTRACT

We introduce a new iterative process which can be seen as a hybrid of Picard and Mann iterative processes. We show that the new process converges faster than all of Picard, Mann and Ishikawa iterative processes in the sense of Berinde (Iterative Approximation of Fixed Points, 2002) for contractions. We support our analytical proof by a numerical example. We prove a strong convergence theorem with the help of our process for the class of nonexpansive mappings in general Banach spaces and apply it to get a result in uniformly convex Banach spaces. Our weak convergence results are proved when the underlying space satisfies Opial’s condition or has Fréchet differentiable norm or its dual satisfies the Kadec-Klee property.MSC:47H10, 54H25. More... »

PAGES

69

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/1687-1812-2013-69

DOI

http://dx.doi.org/10.1186/1687-1812-2013-69

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1001676343


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": "Department of Mathematics, Statistics and Physics, Qatar University, 2713, Doha, State of Qatar", 
          "id": "http://www.grid.ac/institutes/grid.412603.2", 
          "name": [
            "Department of Mathematics, Statistics and Physics, Qatar University, 2713, Doha, State of 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"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf02764907", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011343307", 
          "https://doi.org/10.1007/bf02764907"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2013-03-25", 
    "datePublishedReg": "2013-03-25", 
    "description": "We introduce a new iterative process which can be seen as a hybrid of Picard and Mann iterative processes. We show that the new process converges faster than all of Picard, Mann and Ishikawa iterative processes in the sense of Berinde (Iterative Approximation of Fixed Points, 2002) for contractions. We support our analytical proof by a numerical example. We prove a strong convergence theorem with the help of our process for the class of nonexpansive mappings in general Banach spaces and apply it to get a result in uniformly convex Banach spaces. Our weak convergence results are proved when the underlying space satisfies Opial\u2019s condition or has Fr\u00e9chet differentiable norm or its dual satisfies the Kadec-Klee property.MSC:47H10, 54H25.", 
    "genre": "article", 
    "id": "sg:pub.10.1186/1687-1812-2013-69", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1136165", 
        "issn": [
          "1687-1812", 
          "1687-1820"
        ], 
        "name": "Fixed Point Theory and Applications", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "2013"
      }
    ], 
    "keywords": [
      "contraction", 
      "sense of Berinde", 
      "iterative process", 
      "results", 
      "Picard-Mann hybrid iterative process", 
      "conditions", 
      "process", 
      "help", 
      "class", 
      "mapping", 
      "Mann", 
      "sense", 
      "proof", 
      "space", 
      "norms", 
      "Mann iterative process", 
      "properties", 
      "new iterative process", 
      "hybrids", 
      "Ishikawa iterative process", 
      "example", 
      "strong convergence theorems", 
      "general Banach spaces", 
      "Banach spaces", 
      "Kadec-Klee property", 
      "Picard", 
      "process converges", 
      "converges", 
      "Berinde", 
      "analytical proof", 
      "numerical examples", 
      "convergence theorem", 
      "theorem", 
      "nonexpansive mappings", 
      "uniformly convex Banach spaces", 
      "convex Banach space", 
      "weak convergence results", 
      "convergence results", 
      "Opial's condition", 
      "Fr\u00e9chet differentiable norm", 
      "differentiable norm", 
      "dual satisfies", 
      "satisfies", 
      "hybrid of Picard", 
      "new process converges", 
      "space satisfies Opial\u2019s condition", 
      "satisfies Opial\u2019s condition", 
      "hybrid iterative process"
    ], 
    "name": "A Picard-Mann hybrid iterative process", 
    "pagination": "69", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1001676343"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1186/1687-1812-2013-69"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1186/1687-1812-2013-69", 
      "https://app.dimensions.ai/details/publication/pub.1001676343"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2021-12-01T19:28", 
    "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_596.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1186/1687-1812-2013-69"
  }
]
 

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.10.1186/1687-1812-2013-69'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1186/1687-1812-2013-69'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1186/1687-1812-2013-69'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1186/1687-1812-2013-69'


 

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

110 TRIPLES      22 PREDICATES      74 URIs      65 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1186/1687-1812-2013-69 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N79de32e6ab444a0d820ad60e911503be
4 schema:citation sg:pub.10.1007/bf02764907
5 schema:datePublished 2013-03-25
6 schema:datePublishedReg 2013-03-25
7 schema:description We introduce a new iterative process which can be seen as a hybrid of Picard and Mann iterative processes. We show that the new process converges faster than all of Picard, Mann and Ishikawa iterative processes in the sense of Berinde (Iterative Approximation of Fixed Points, 2002) for contractions. We support our analytical proof by a numerical example. We prove a strong convergence theorem with the help of our process for the class of nonexpansive mappings in general Banach spaces and apply it to get a result in uniformly convex Banach spaces. Our weak convergence results are proved when the underlying space satisfies Opial’s condition or has Fréchet differentiable norm or its dual satisfies the Kadec-Klee property.MSC:47H10, 54H25.
8 schema:genre article
9 schema:inLanguage en
10 schema:isAccessibleForFree true
11 schema:isPartOf N74ba72df35bd47b88d986e09b8c247fd
12 N888adb65e329433f84d99c86894e6d3f
13 sg:journal.1136165
14 schema:keywords Banach spaces
15 Berinde
16 Fréchet differentiable norm
17 Ishikawa iterative process
18 Kadec-Klee property
19 Mann
20 Mann iterative process
21 Opial's condition
22 Picard
23 Picard-Mann hybrid iterative process
24 analytical proof
25 class
26 conditions
27 contraction
28 convergence results
29 convergence theorem
30 converges
31 convex Banach space
32 differentiable norm
33 dual satisfies
34 example
35 general Banach spaces
36 help
37 hybrid iterative process
38 hybrid of Picard
39 hybrids
40 iterative process
41 mapping
42 new iterative process
43 new process converges
44 nonexpansive mappings
45 norms
46 numerical examples
47 process
48 process converges
49 proof
50 properties
51 results
52 satisfies
53 satisfies Opial’s condition
54 sense
55 sense of Berinde
56 space
57 space satisfies Opial’s condition
58 strong convergence theorems
59 theorem
60 uniformly convex Banach spaces
61 weak convergence results
62 schema:name A Picard-Mann hybrid iterative process
63 schema:pagination 69
64 schema:productId N1647a8ead7694592b9c274c4bd5c1d75
65 N71a9fd2ecc224702831ab024868abe04
66 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001676343
67 https://doi.org/10.1186/1687-1812-2013-69
68 schema:sdDatePublished 2021-12-01T19:28
69 schema:sdLicense https://scigraph.springernature.com/explorer/license/
70 schema:sdPublisher N2bb77575ba2c40f48c99b75bac8dcf3c
71 schema:url https://doi.org/10.1186/1687-1812-2013-69
72 sgo:license sg:explorer/license/
73 sgo:sdDataset articles
74 rdf:type schema:ScholarlyArticle
75 N1647a8ead7694592b9c274c4bd5c1d75 schema:name doi
76 schema:value 10.1186/1687-1812-2013-69
77 rdf:type schema:PropertyValue
78 N2bb77575ba2c40f48c99b75bac8dcf3c schema:name Springer Nature - SN SciGraph project
79 rdf:type schema:Organization
80 N71a9fd2ecc224702831ab024868abe04 schema:name dimensions_id
81 schema:value pub.1001676343
82 rdf:type schema:PropertyValue
83 N74ba72df35bd47b88d986e09b8c247fd schema:issueNumber 1
84 rdf:type schema:PublicationIssue
85 N79de32e6ab444a0d820ad60e911503be rdf:first sg:person.010266761613.61
86 rdf:rest rdf:nil
87 N888adb65e329433f84d99c86894e6d3f schema:volumeNumber 2013
88 rdf:type schema:PublicationVolume
89 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
90 schema:name Mathematical Sciences
91 rdf:type schema:DefinedTerm
92 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
93 schema:name Pure Mathematics
94 rdf:type schema:DefinedTerm
95 sg:journal.1136165 schema:issn 1687-1812
96 1687-1820
97 schema:name Fixed Point Theory and Applications
98 schema:publisher Springer Nature
99 rdf:type schema:Periodical
100 sg:person.010266761613.61 schema:affiliation grid-institutes:grid.412603.2
101 schema:familyName Khan
102 schema:givenName Safeer Hussain
103 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010266761613.61
104 rdf:type schema:Person
105 sg:pub.10.1007/bf02764907 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011343307
106 https://doi.org/10.1007/bf02764907
107 rdf:type schema:CreativeWork
108 grid-institutes:grid.412603.2 schema:alternateName Department of Mathematics, Statistics and Physics, Qatar University, 2713, Doha, State of Qatar
109 schema:name Department of Mathematics, Statistics and Physics, Qatar University, 2713, Doha, State of Qatar
110 rdf:type schema:Organization
 




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


...