On some new generalized fractional inequalities for twice differentiable functions View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2022-06-30

AUTHORS

Hüseyin Budak, Melike Yavuz, Hasan Kara

ABSTRACT

In this paper, we establish an identity involving Sarikaya fractional integrals for twice differentiable functions. We obtain some new generalized fractional inequalities for the functions whose second derivatives in absolute value are convex by utilizing obtained equality. Utilizing the new inequalities obtained, some new inequalities for Riemann–Liouville fractional integrals and k-Riemann–Liouville fractional integrals are obtained. In addition, some of these results generalize ones obtained in earlier works. More... »

PAGES

507-519

References to SciGraph publications

  • 2021-10-18. New version of fractional Simpson type inequalities for twice differentiable functions in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2021-10-29. On the fractional integral inclusions having exponential kernels for interval-valued convex functions in MATHEMATICAL SCIENCES
  • 2019-05-02. Simpson type integral inequalities for generalized fractional integral in REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A. MATEMÁTICAS
  • 2012-10-29. Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s40065-022-00381-1

    DOI

    http://dx.doi.org/10.1007/s40065-022-00381-1

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1149110420


    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, Faculty of Science and Arts, D\u00fczce University, D\u00fczce, Turkey", 
              "id": "http://www.grid.ac/institutes/grid.412121.5", 
              "name": [
                "Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce, Turkey"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Budak", 
            "givenName": "H\u00fcseyin", 
            "id": "sg:person.07356663407.38", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07356663407.38"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce, Turkey", 
              "id": "http://www.grid.ac/institutes/grid.412121.5", 
              "name": [
                "Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce, Turkey"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yavuz", 
            "givenName": "Melike", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce, Turkey", 
              "id": "http://www.grid.ac/institutes/grid.412121.5", 
              "name": [
                "Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce, Turkey"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Kara", 
            "givenName": "Hasan", 
            "id": "sg:person.011764036051.61", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011764036051.61"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1186/s13662-021-03615-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1141971522", 
              "https://doi.org/10.1186/s13662-021-03615-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1186/1029-242x-2012-247", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028833101", 
              "https://doi.org/10.1186/1029-242x-2012-247"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s13398-019-00680-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1113877940", 
              "https://doi.org/10.1007/s13398-019-00680-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s40096-021-00445-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1142258082", 
              "https://doi.org/10.1007/s40096-021-00445-x"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2022-06-30", 
        "datePublishedReg": "2022-06-30", 
        "description": "In this paper, we establish an identity involving Sarikaya fractional integrals for twice differentiable functions. We obtain some new generalized fractional inequalities for the functions whose second derivatives in absolute value are convex by utilizing obtained equality. Utilizing the new inequalities obtained, some new inequalities for Riemann\u2013Liouville fractional integrals and k-Riemann\u2013Liouville fractional integrals are obtained. In addition, some of these results generalize ones obtained in earlier works.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s40065-022-00381-1", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136844", 
            "issn": [
              "2193-5343", 
              "2193-5351"
            ], 
            "name": "Arabian Journal of Mathematics", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "11"
          }
        ], 
        "keywords": [
          "fractional integrals", 
          "differentiable functions", 
          "fractional inequalities", 
          "Riemann\u2013Liouville fractional integral", 
          "new inequalities", 
          "second derivative", 
          "integrals", 
          "inequality", 
          "earlier work", 
          "absolute value", 
          "function", 
          "one", 
          "equality", 
          "derivatives", 
          "work", 
          "results", 
          "values", 
          "addition", 
          "identity", 
          "paper"
        ], 
        "name": "On some new generalized fractional inequalities for twice differentiable functions", 
        "pagination": "507-519", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1149110420"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s40065-022-00381-1"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s40065-022-00381-1", 
          "https://app.dimensions.ai/details/publication/pub.1149110420"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-12-01T06:45", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20221201/entities/gbq_results/article/article_954.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s40065-022-00381-1"
      }
    ]
     

    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/s40065-022-00381-1'

    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/s40065-022-00381-1'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s40065-022-00381-1'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s40065-022-00381-1'


     

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

    106 TRIPLES      21 PREDICATES      48 URIs      36 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s40065-022-00381-1 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N9d0c75b984e84bd792ca9704f97cdd20
    4 schema:citation sg:pub.10.1007/s13398-019-00680-x
    5 sg:pub.10.1007/s40096-021-00445-x
    6 sg:pub.10.1186/1029-242x-2012-247
    7 sg:pub.10.1186/s13662-021-03615-2
    8 schema:datePublished 2022-06-30
    9 schema:datePublishedReg 2022-06-30
    10 schema:description In this paper, we establish an identity involving Sarikaya fractional integrals for twice differentiable functions. We obtain some new generalized fractional inequalities for the functions whose second derivatives in absolute value are convex by utilizing obtained equality. Utilizing the new inequalities obtained, some new inequalities for Riemann–Liouville fractional integrals and k-Riemann–Liouville fractional integrals are obtained. In addition, some of these results generalize ones obtained in earlier works.
    11 schema:genre article
    12 schema:isAccessibleForFree true
    13 schema:isPartOf N236617a5a7d14f949fe677ff65d68a59
    14 Nac024c68faa941e5a03cf3326d10a154
    15 sg:journal.1136844
    16 schema:keywords Riemann–Liouville fractional integral
    17 absolute value
    18 addition
    19 derivatives
    20 differentiable functions
    21 earlier work
    22 equality
    23 fractional inequalities
    24 fractional integrals
    25 function
    26 identity
    27 inequality
    28 integrals
    29 new inequalities
    30 one
    31 paper
    32 results
    33 second derivative
    34 values
    35 work
    36 schema:name On some new generalized fractional inequalities for twice differentiable functions
    37 schema:pagination 507-519
    38 schema:productId N4d54df6b5f8542db86189f3023c520d6
    39 N97a924637bae422b9f7b15ae0f443672
    40 schema:sameAs https://app.dimensions.ai/details/publication/pub.1149110420
    41 https://doi.org/10.1007/s40065-022-00381-1
    42 schema:sdDatePublished 2022-12-01T06:45
    43 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    44 schema:sdPublisher N6e25dd22a94347d5a98eeabfd4263686
    45 schema:url https://doi.org/10.1007/s40065-022-00381-1
    46 sgo:license sg:explorer/license/
    47 sgo:sdDataset articles
    48 rdf:type schema:ScholarlyArticle
    49 N236617a5a7d14f949fe677ff65d68a59 schema:issueNumber 3
    50 rdf:type schema:PublicationIssue
    51 N4d54df6b5f8542db86189f3023c520d6 schema:name dimensions_id
    52 schema:value pub.1149110420
    53 rdf:type schema:PropertyValue
    54 N66f0b5bb0a8d4b6eacac1d5f4886eb8c rdf:first Nb0a3b7e4a46c40ce8b93c6a78c98f277
    55 rdf:rest Nf4b7e1d26bf740ec905d56eec1f152f5
    56 N6e25dd22a94347d5a98eeabfd4263686 schema:name Springer Nature - SN SciGraph project
    57 rdf:type schema:Organization
    58 N97a924637bae422b9f7b15ae0f443672 schema:name doi
    59 schema:value 10.1007/s40065-022-00381-1
    60 rdf:type schema:PropertyValue
    61 N9d0c75b984e84bd792ca9704f97cdd20 rdf:first sg:person.07356663407.38
    62 rdf:rest N66f0b5bb0a8d4b6eacac1d5f4886eb8c
    63 Nac024c68faa941e5a03cf3326d10a154 schema:volumeNumber 11
    64 rdf:type schema:PublicationVolume
    65 Nb0a3b7e4a46c40ce8b93c6a78c98f277 schema:affiliation grid-institutes:grid.412121.5
    66 schema:familyName Yavuz
    67 schema:givenName Melike
    68 rdf:type schema:Person
    69 Nf4b7e1d26bf740ec905d56eec1f152f5 rdf:first sg:person.011764036051.61
    70 rdf:rest rdf:nil
    71 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    72 schema:name Mathematical Sciences
    73 rdf:type schema:DefinedTerm
    74 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    75 schema:name Pure Mathematics
    76 rdf:type schema:DefinedTerm
    77 sg:journal.1136844 schema:issn 2193-5343
    78 2193-5351
    79 schema:name Arabian Journal of Mathematics
    80 schema:publisher Springer Nature
    81 rdf:type schema:Periodical
    82 sg:person.011764036051.61 schema:affiliation grid-institutes:grid.412121.5
    83 schema:familyName Kara
    84 schema:givenName Hasan
    85 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011764036051.61
    86 rdf:type schema:Person
    87 sg:person.07356663407.38 schema:affiliation grid-institutes:grid.412121.5
    88 schema:familyName Budak
    89 schema:givenName Hüseyin
    90 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07356663407.38
    91 rdf:type schema:Person
    92 sg:pub.10.1007/s13398-019-00680-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1113877940
    93 https://doi.org/10.1007/s13398-019-00680-x
    94 rdf:type schema:CreativeWork
    95 sg:pub.10.1007/s40096-021-00445-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1142258082
    96 https://doi.org/10.1007/s40096-021-00445-x
    97 rdf:type schema:CreativeWork
    98 sg:pub.10.1186/1029-242x-2012-247 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028833101
    99 https://doi.org/10.1186/1029-242x-2012-247
    100 rdf:type schema:CreativeWork
    101 sg:pub.10.1186/s13662-021-03615-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1141971522
    102 https://doi.org/10.1186/s13662-021-03615-2
    103 rdf:type schema:CreativeWork
    104 grid-institutes:grid.412121.5 schema:alternateName Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
    105 schema:name Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
    106 rdf:type schema:Organization
     




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


    ...