Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals

In the paper, based on Erdélyi-Kober fractional integrals $ ^\rho \mathcal{K}^\alpha_{\chi+}f $ and $ ^\rho \mathcal{K}^\alpha_{\chi-}f $ for any $ \chi\in[a, b] $ with $ f\in\mathfrak{X}_c^p(a, b) $, authors establish some new Hermite-Hadamard type inequalities for convex function. The obtained ine...

Full description

Saved in:
Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 10; pp. 11494 - 11507
Main Authors Hai, XuRan, Wang, ShuHong
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
convex function
erdélyi-kober fractional integrals
error estimations
hermite-hadamard inequality
riemann-liouville fractional integrals
Online AccessGet full text

Cover

Abstract In the paper, based on Erdélyi-Kober fractional integrals $ ^\rho \mathcal{K}^\alpha_{\chi+}f $ and $ ^\rho \mathcal{K}^\alpha_{\chi-}f $ for any $ \chi\in[a, b] $ with $ f\in\mathfrak{X}_c^p(a, b) $, authors establish some new Hermite-Hadamard type inequalities for convex function. The obtained inequalities generalize the corresponding results for Riemann-Liouville fractional integrals by taking limits when a parameter $ \rho\rightarrow1 $. As applications, the error estimations of Hermite-Hadamard type inequality are also provided.
AbstractList In the paper, based on Erdélyi-Kober fractional integrals $ ^\rho \mathcal{K}^\alpha_{\chi+}f $ and $ ^\rho \mathcal{K}^\alpha_{\chi-}f $ for any $ \chi\in[a, b] $ with $ f\in\mathfrak{X}_c^p(a, b) $, authors establish some new Hermite-Hadamard type inequalities for convex function. The obtained inequalities generalize the corresponding results for Riemann-Liouville fractional integrals by taking limits when a parameter $ \rho\rightarrow1 $. As applications, the error estimations of Hermite-Hadamard type inequality are also provided.
Author Wang, ShuHong
Hai, XuRan
Author_xml – sequence: 1
  givenname: XuRan
  surname: Hai
  fullname: Hai, XuRan
– sequence: 2
  givenname: ShuHong
  surname: Wang
  fullname: Wang, ShuHong
BookMark eNptUMtOwzAQtFCRKKU3PiAfQIpfsZMjqgqtqMQBOFsbe9O6SpPimEM_ie_gx0hpkRDisrNazYxm55IMmrZBQq4ZnYhCyNstxPWEU86UUmdkyKUWqSryfPBrvyDjrttQ2rO45FoOyfMcw9ZHTOfgYAvBJXG_w8Q3-PYOtY8eu6SEDl3SNklcYzIL7vOj3vv0sS0xJFUAG33bQN1rIq4C1N0VOa96wPEJR-T1fvYynafLp4fF9G6ZWqHzmCrJBS0zySrAMkNAJ7iiOc21kq6seGYZE4xmZcG1ljqHzDpE5hQ6BcI6MSKLo69rYWN2wff596YFb74PbVgZCNHbGo3lmSorIZzOhETFiqIfZa5lnhVWFbT34kcvG9quC1gZ6yMcPosBfG0YNYeWzaFlc2q5F938Ef2E-Jf-BXQbgYM
CitedBy_id crossref_primary_10_3390_math11081953
Cites_doi 10.1007/978-3-319-52141-1
10.1155/S102558340000031X
10.1006/jath.2001.3658
10.1515/mjpaa-2017-0003
10.20944/preprints201609.0105.v1
10.1007/s13398-019-00680-x
10.1007/BF02189414
10.1186/s13662-017-1306-z
10.1016/j.jmaa.2016.09.018
10.1007/978-1-4020-6042-7
10.1002/mma.5893
10.1137/S0036142903435958
10.2298/FIL1715989C
10.1016/j.amc.2011.03.062
10.1090/S0025-5718-03-01622-3
ContentType Journal Article
CorporateAuthor College of Mathematics and Physics, Inner Mongolia Minzu University, Tongliao 028000, China
CorporateAuthor_xml – name: College of Mathematics and Physics, Inner Mongolia Minzu University, Tongliao 028000, China
DBID AAYXX
CITATION
DOA
DOI 10.3934/math.2021666
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 2473-6988
EndPage 11507
ExternalDocumentID oai_doaj_org_article_c256bf33d7534e6199e61b874859c690
10_3934_math_2021666
GroupedDBID AAYXX
ADBBV
ALMA_UNASSIGNED_HOLDINGS
AMVHM
BCNDV
CITATION
EBS
FRJ
GROUPED_DOAJ
IAO
ITC
M~E
OK1
RAN
ID FETCH-LOGICAL-c378t-64230b541faeb5eaed3260808764dbf25c113105b9277478a5cdee1d6ed6a3cd3
IEDL.DBID DOA
ISSN 2473-6988
IngestDate Wed Aug 27 01:30:59 EDT 2025
Thu Apr 24 22:52:27 EDT 2025
Tue Jul 01 03:56:49 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 10
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c378t-64230b541faeb5eaed3260808764dbf25c113105b9277478a5cdee1d6ed6a3cd3
OpenAccessLink https://doaj.org/article/c256bf33d7534e6199e61b874859c690
PageCount 14
ParticipantIDs doaj_primary_oai_doaj_org_article_c256bf33d7534e6199e61b874859c690
crossref_citationtrail_10_3934_math_2021666
crossref_primary_10_3934_math_2021666
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2021-01-01
PublicationDateYYYYMMDD 2021-01-01
PublicationDate_xml – month: 01
  year: 2021
  text: 2021-01-01
  day: 01
PublicationDecade 2020
PublicationTitle AIMS mathematics
PublicationYear 2021
Publisher AIMS Press
Publisher_xml – name: AIMS Press
References key-10.3934/math.2021666-14
key-10.3934/math.2021666-15
key-10.3934/math.2021666-12
key-10.3934/math.2021666-23
key-10.3934/math.2021666-13
key-10.3934/math.2021666-24
key-10.3934/math.2021666-10
key-10.3934/math.2021666-21
key-10.3934/math.2021666-11
key-10.3934/math.2021666-22
key-10.3934/math.2021666-20
key-10.3934/math.2021666-8
key-10.3934/math.2021666-7
key-10.3934/math.2021666-9
key-10.3934/math.2021666-4
key-10.3934/math.2021666-18
key-10.3934/math.2021666-3
key-10.3934/math.2021666-19
key-10.3934/math.2021666-6
key-10.3934/math.2021666-16
key-10.3934/math.2021666-5
key-10.3934/math.2021666-17
key-10.3934/math.2021666-2
key-10.3934/math.2021666-1
References_xml – ident: key-10.3934/math.2021666-12
– ident: key-10.3934/math.2021666-13
– ident: key-10.3934/math.2021666-1
  doi: 10.1007/978-3-319-52141-1
– ident: key-10.3934/math.2021666-7
  doi: 10.1155/S102558340000031X
– ident: key-10.3934/math.2021666-11
  doi: 10.1006/jath.2001.3658
– ident: key-10.3934/math.2021666-24
  doi: 10.1515/mjpaa-2017-0003
– ident: key-10.3934/math.2021666-3
  doi: 10.20944/preprints201609.0105.v1
– ident: key-10.3934/math.2021666-8
  doi: 10.1007/s13398-019-00680-x
– ident: key-10.3934/math.2021666-19
  doi: 10.1007/BF02189414
– ident: key-10.3934/math.2021666-15
  doi: 10.1186/s13662-017-1306-z
– ident: key-10.3934/math.2021666-5
  doi: 10.1016/j.jmaa.2016.09.018
– ident: key-10.3934/math.2021666-21
  doi: 10.1007/978-1-4020-6042-7
– ident: key-10.3934/math.2021666-23
– ident: key-10.3934/math.2021666-6
  doi: 10.1002/mma.5893
– ident: key-10.3934/math.2021666-9
  doi: 10.1137/S0036142903435958
– ident: key-10.3934/math.2021666-22
– ident: key-10.3934/math.2021666-20
– ident: key-10.3934/math.2021666-4
  doi: 10.2298/FIL1715989C
– ident: key-10.3934/math.2021666-17
– ident: key-10.3934/math.2021666-2
– ident: key-10.3934/math.2021666-14
– ident: key-10.3934/math.2021666-16
  doi: 10.1016/j.amc.2011.03.062
– ident: key-10.3934/math.2021666-10
  doi: 10.1090/S0025-5718-03-01622-3
– ident: key-10.3934/math.2021666-18
SSID ssj0002124274
Score 2.1386082
Snippet In the paper, based on Erdélyi-Kober fractional integrals $ ^\rho \mathcal{K}^\alpha_{\chi+}f $ and $ ^\rho \mathcal{K}^\alpha_{\chi-}f $ for any $ \chi\in[a,...
SourceID doaj
crossref
SourceType Open Website
Enrichment Source
Index Database
StartPage 11494
SubjectTerms convex function
erdélyi-kober fractional integrals
error estimations
hermite-hadamard inequality
riemann-liouville fractional integrals
Title Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals
URI https://doaj.org/article/c256bf33d7534e6199e61b874859c690
Volume 6
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELZQJxgQT1Fe8gATsprUzsMjoFYVqCxQqVvkx0VCKilqw8BP4nfwx7iLQ1UGxMKSIbok1nfR3Xf2-TNjFybKwcQQC-lcLhQkXuhMOuEBs4lV2upGZ3b8kI4m6m6aTNeO-qKesCAPHIDrOczJtpTSI69WgHRf48XmmcoT7bC0o-iLOW-tmKIYjAFZYb0VOt2llqqH_I_WHvq0TPYjB61J9Tc5ZbjDtlsyyK_DIHbZBlR7bGu8UlJd7rPHEXWr1CAwRJgXdCenSVOO3DBsh8RCl1Mm8nxecXyODxb-82P2_izuqWeal4uwcwE_0ypDzJYHbDIcPN2ORHsQgnAyy2uBNYKMbKLi0oBNwIBH0oVUDyOZ8rbsJy6OkaYlBCzp4ZvEeYDYp-BTI52Xh6xTzSs4Ytwbj5zB9bUzqUrBaWWyyLg8p27QKIUuu_qGpnCtSjgdVjErsFogIAsCsmiB7LLLlfVrUMf4xe6GUF7ZkKZ1cwM9XbSeLv7y9PF_vOSEbdKYwiTKKevUizc4Q1pR2_PmD_oC8yXL0A
linkProvider Directory of Open Access Journals
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Hermite-Hadamard+type+inequalities+based+on+the+Erd%C3%A9lyi-Kober+fractional+integrals&rft.jtitle=AIMS+mathematics&rft.au=XuRan+Hai&rft.au=ShuHong+Wang&rft.date=2021-01-01&rft.pub=AIMS+Press&rft.eissn=2473-6988&rft.volume=6&rft.issue=10&rft.spage=11494&rft.epage=11507&rft_id=info:doi/10.3934%2Fmath.2021666&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_c256bf33d7534e6199e61b874859c690
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2473-6988&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2473-6988&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2473-6988&client=summon