Some well known inequalities for $ (h_1, h_2) $-convex stochastic process via interval set inclusion relation

This note introduces the concept of $ (h_1, h_2) $-convex stochastic processes using interval-valued functions. First we develop Hermite-Hadmard $ (\mathbb{H.H}) $ type inequalities, then we check the results for the product of two convex stochastic process mappings, and finally we develop Ostrowski...

Full description

Saved in:
Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 9; pp. 19913 - 19932
Main Authors Afzal, Waqar, Abbas, Mujahid, Eldin, Sayed M., Khan, Zareen A.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
hermite-hadamard inequality
interval valued functions
jensen inequality
ostrowski inequality
stochastic process
Online AccessGet full text

Cover

Abstract This note introduces the concept of $ (h_1, h_2) $-convex stochastic processes using interval-valued functions. First we develop Hermite-Hadmard $ (\mathbb{H.H}) $ type inequalities, then we check the results for the product of two convex stochastic process mappings, and finally we develop Ostrowski and Jensen type inequalities for $ (h_1, h_2) $-convex stochastic process. Also, we have shown that this is a more generalized and larger class of convex stochastic processes with some remark. Furthermore, we validate our main findings by providing some non-trivial examples.
AbstractList This note introduces the concept of $ (h_1, h_2) $-convex stochastic processes using interval-valued functions. First we develop Hermite-Hadmard $ (\mathbb{H.H}) $ type inequalities, then we check the results for the product of two convex stochastic process mappings, and finally we develop Ostrowski and Jensen type inequalities for $ (h_1, h_2) $-convex stochastic process. Also, we have shown that this is a more generalized and larger class of convex stochastic processes with some remark. Furthermore, we validate our main findings by providing some non-trivial examples.
Author Khan, Zareen A.
Afzal, Waqar
Eldin, Sayed M.
Abbas, Mujahid
Author_xml – sequence: 1
  givenname: Waqar
  surname: Afzal
  fullname: Afzal, Waqar
  organization: Department of Mathemtics, Government College University Lahore (GCUL), Lahore 54000, Pakistan
– sequence: 2
  givenname: Mujahid
  surname: Abbas
  fullname: Abbas, Mujahid
  organization: Department of Mathemtics, Government College University Lahore (GCUL), Lahore 54000, Pakistan, Department of Medical Research, China Medical University, Taichung, Taiwan, Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa
– sequence: 3
  givenname: Sayed M.
  surname: Eldin
  fullname: Eldin, Sayed M.
  organization: Center of Research, Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt
– sequence: 4
  givenname: Zareen A.
  surname: Khan
  fullname: Khan, Zareen A.
  organization: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
BookMark eNp1UD1PHTEQtCIihQBlehcUROLAX3dnlxEiCRISBUlt7dlrnsHvDLZ5JP-eAwKKIqXaD83M7sxHsjXnGQn5xNmRNFIdr6GtjgQTkjPevyPbQo2yG4zWW3_1H8herdeMMcGFEqPaJuvLvEb6gCnRmzk_zDTOeHcPKbaIlYZc6D49WFl-SFdWfKb7ncvzBn_R2rJbQW3R0duSHdZKNxEWdsOygUQrtmVw6b7GPNOCCdrS7JL3AVLFvT91h_z8evrj5Ht3fvHt7OTLeeek5q0TAGiY8lpMzi92RheUH9wgRK-1C8OkPTNu4IaDCpM3TPt-wLHnxkyCaSd3yNmLrs9wbW9LXEP5bTNE-7zI5cpCWX5PaBVfTgqvUIFXQbpJwdgHL0MwfT_iuGh1L1qu5FoLhjc9zuxT9PYpevsa_YKX_-BdbM_uW4GY_sN6BBxSinc
CitedBy_id crossref_primary_10_2478_ama_2024_0016
crossref_primary_10_3390_fractalfract7090687
crossref_primary_10_3934_mbe_2024151
crossref_primary_10_3390_math12030382
crossref_primary_10_3934_math_2024778
crossref_primary_10_3934_math_2024249
Cites_doi 10.1080/09720502.2021.1938994
10.1186/s13660-021-02619-6
10.3390/sym13040568
10.15559/18-VMSTA117
10.1080/03610926.2020.1865403
10.1063/1.5143908
10.1016/j.jsv.2013.12.015
10.3934/math.2023366
10.3390/sym15040831
10.3934/jimo.2018063
10.1080/09720502.2021.1887607
10.1007/BF02190513
10.3934/math.2020315
10.55730/1300-0098.3263
10.2991/ijcis.d.210620.001
10.12691/tjant-2-6-3
10.3390/fractalfract6090518
10.3934/math.2023683
10.1109/TNN.2008.2011267
10.1186/s13662-020-02977-3
10.20852/ntmsci.2019.376
10.3934/math.2021371
10.11121/ijocta.01.2019.00602
10.3934/math.20221064
10.3934/math.2023170
10.1186/1029-242X-2013-326
10.3934/math.2023160
10.1186/s13660-018-1896-3
10.1007/s00500-017-2818-x
10.1186/s13662-021-03245-8
10.1007/s00010-011-0090-1
10.1186/s13660-020-02393-x
10.1016/j.envsoft.2011.10.007
10.3934/math.2023087
10.3390/math10234540
10.1063/5.0039672
10.1186/s13662-020-02782-y
10.1155/2022/3830324
10.29020/nybg.ejpam.v16i1.4689
10.1007/BF01830983
10.18576/amis/120104
10.1007/s00010-017-0488-5
10.3390/math10244777
10.3390/math10162970
10.3934/math.2023168
10.1063/5.0008964
10.18576/amis/22nuevoformat20(1)2
10.3934/math.2023817
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.3934/math.20231015
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 19932
ExternalDocumentID oai_doaj_org_article_413812d4e4ad4f3cb4a75fd3ff9557e7
10_3934_math_20231015
GroupedDBID AAYXX
ADBBV
ALMA_UNASSIGNED_HOLDINGS
AMVHM
BCNDV
CITATION
EBS
FRJ
GROUPED_DOAJ
IAO
ITC
M~E
OK1
RAN
ID FETCH-LOGICAL-c381t-2aae904d82bcd0157cf4d6c622588cf6b8d09c6191a4fbd908d56e75199b208c3
IEDL.DBID DOA
ISSN 2473-6988
IngestDate Wed Aug 27 01:28:17 EDT 2025
Thu Apr 24 23:02:15 EDT 2025
Tue Jul 01 03:57:03 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 9
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c381t-2aae904d82bcd0157cf4d6c622588cf6b8d09c6191a4fbd908d56e75199b208c3
OpenAccessLink https://doaj.org/article/413812d4e4ad4f3cb4a75fd3ff9557e7
PageCount 20
ParticipantIDs doaj_primary_oai_doaj_org_article_413812d4e4ad4f3cb4a75fd3ff9557e7
crossref_primary_10_3934_math_20231015
crossref_citationtrail_10_3934_math_20231015
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2023-01-01
PublicationDateYYYYMMDD 2023-01-01
PublicationDate_xml – month: 01
  year: 2023
  text: 2023-01-01
  day: 01
PublicationDecade 2020
PublicationTitle AIMS mathematics
PublicationYear 2023
Publisher AIMS Press
Publisher_xml – name: AIMS Press
References key-10.3934/math.20231015-51
key-10.3934/math.20231015-52
key-10.3934/math.20231015-53
key-10.3934/math.20231015-10
key-10.3934/math.20231015-54
key-10.3934/math.20231015-11
key-10.3934/math.20231015-55
key-10.3934/math.20231015-12
key-10.3934/math.20231015-56
key-10.3934/math.20231015-13
key-10.3934/math.20231015-14
key-10.3934/math.20231015-50
key-10.3934/math.20231015-15
key-10.3934/math.20231015-16
key-10.3934/math.20231015-17
key-10.3934/math.20231015-18
key-10.3934/math.20231015-19
key-10.3934/math.20231015-20
key-10.3934/math.20231015-21
key-10.3934/math.20231015-22
key-10.3934/math.20231015-23
key-10.3934/math.20231015-24
key-10.3934/math.20231015-25
key-10.3934/math.20231015-26
key-10.3934/math.20231015-27
key-10.3934/math.20231015-28
key-10.3934/math.20231015-29
key-10.3934/math.20231015-1
key-10.3934/math.20231015-30
key-10.3934/math.20231015-2
key-10.3934/math.20231015-31
key-10.3934/math.20231015-3
key-10.3934/math.20231015-32
key-10.3934/math.20231015-33
key-10.3934/math.20231015-34
key-10.3934/math.20231015-35
key-10.3934/math.20231015-36
key-10.3934/math.20231015-8
key-10.3934/math.20231015-9
key-10.3934/math.20231015-4
key-10.3934/math.20231015-5
key-10.3934/math.20231015-6
key-10.3934/math.20231015-7
key-10.3934/math.20231015-37
key-10.3934/math.20231015-38
key-10.3934/math.20231015-39
key-10.3934/math.20231015-40
key-10.3934/math.20231015-41
key-10.3934/math.20231015-42
key-10.3934/math.20231015-43
key-10.3934/math.20231015-44
key-10.3934/math.20231015-45
key-10.3934/math.20231015-46
key-10.3934/math.20231015-47
key-10.3934/math.20231015-48
key-10.3934/math.20231015-49
References_xml – ident: key-10.3934/math.20231015-30
– ident: key-10.3934/math.20231015-12
  doi: 10.1080/09720502.2021.1938994
– ident: key-10.3934/math.20231015-35
  doi: 10.1186/s13660-021-02619-6
– ident: key-10.3934/math.20231015-53
  doi: 10.3390/sym13040568
– ident: key-10.3934/math.20231015-17
  doi: 10.15559/18-VMSTA117
– ident: key-10.3934/math.20231015-16
  doi: 10.1080/03610926.2020.1865403
– ident: key-10.3934/math.20231015-36
  doi: 10.1063/1.5143908
– ident: key-10.3934/math.20231015-11
– ident: key-10.3934/math.20231015-55
  doi: 10.1016/j.jsv.2013.12.015
– ident: key-10.3934/math.20231015-25
  doi: 10.3934/math.2023366
– ident: key-10.3934/math.20231015-14
  doi: 10.3390/sym15040831
– ident: key-10.3934/math.20231015-3
  doi: 10.3934/jimo.2018063
– ident: key-10.3934/math.20231015-15
  doi: 10.1080/09720502.2021.1887607
– ident: key-10.3934/math.20231015-5
  doi: 10.1007/BF02190513
– ident: key-10.3934/math.20231015-46
  doi: 10.3934/math.2020315
– ident: key-10.3934/math.20231015-19
  doi: 10.55730/1300-0098.3263
– ident: key-10.3934/math.20231015-39
  doi: 10.2991/ijcis.d.210620.001
– ident: key-10.3934/math.20231015-9
  doi: 10.12691/tjant-2-6-3
– ident: key-10.3934/math.20231015-50
  doi: 10.3390/fractalfract6090518
– ident: key-10.3934/math.20231015-18
  doi: 10.3934/math.2023683
– ident: key-10.3934/math.20231015-4
  doi: 10.1109/TNN.2008.2011267
– ident: key-10.3934/math.20231015-33
  doi: 10.1186/s13662-020-02977-3
– ident: key-10.3934/math.20231015-10
  doi: 10.20852/ntmsci.2019.376
– ident: key-10.3934/math.20231015-28
  doi: 10.3934/math.2021371
– ident: key-10.3934/math.20231015-8
  doi: 10.11121/ijocta.01.2019.00602
– ident: key-10.3934/math.20231015-20
  doi: 10.1080/03610926.2020.1865403
– ident: key-10.3934/math.20231015-49
  doi: 10.3934/math.20221064
– ident: key-10.3934/math.20231015-48
  doi: 10.3934/math.2023170
– ident: key-10.3934/math.20231015-22
  doi: 10.1186/1029-242X-2013-326
– ident: key-10.3934/math.20231015-52
  doi: 10.3934/math.2023160
– ident: key-10.3934/math.20231015-24
  doi: 10.1186/s13660-018-1896-3
– ident: key-10.3934/math.20231015-2
  doi: 10.1007/s00500-017-2818-x
– ident: key-10.3934/math.20231015-37
  doi: 10.1186/s13662-021-03245-8
– ident: key-10.3934/math.20231015-7
  doi: 10.1007/s00010-011-0090-1
– ident: key-10.3934/math.20231015-34
  doi: 10.1186/s13660-020-02393-x
– ident: key-10.3934/math.20231015-56
  doi: 10.1016/j.envsoft.2011.10.007
– ident: key-10.3934/math.20231015-31
  doi: 10.3934/math.2023087
– ident: key-10.3934/math.20231015-42
  doi: 10.3390/math10234540
– ident: key-10.3934/math.20231015-1
– ident: key-10.3934/math.20231015-23
– ident: key-10.3934/math.20231015-26
  doi: 10.3934/math.2023366
– ident: key-10.3934/math.20231015-45
  doi: 10.1063/5.0039672
– ident: key-10.3934/math.20231015-38
  doi: 10.1186/s13662-020-02782-y
– ident: key-10.3934/math.20231015-47
  doi: 10.1155/2022/3830324
– ident: key-10.3934/math.20231015-43
  doi: 10.29020/nybg.ejpam.v16i1.4689
– ident: key-10.3934/math.20231015-6
  doi: 10.1007/BF01830983
– ident: key-10.3934/math.20231015-27
  doi: 10.18576/amis/120104
– ident: key-10.3934/math.20231015-32
  doi: 10.1007/s00010-017-0488-5
– ident: key-10.3934/math.20231015-41
  doi: 10.3390/math10244777
– ident: key-10.3934/math.20231015-54
  doi: 10.1016/j.jsv.2013.12.015
– ident: key-10.3934/math.20231015-51
  doi: 10.3390/math10162970
– ident: key-10.3934/math.20231015-44
  doi: 10.3934/math.2023168
– ident: key-10.3934/math.20231015-40
  doi: 10.1063/5.0008964
– ident: key-10.3934/math.20231015-29
  doi: 10.3934/math.2021371
– ident: key-10.3934/math.20231015-13
  doi: 10.18576/amis/22nuevoformat20(1)2
– ident: key-10.3934/math.20231015-21
  doi: 10.3934/math.2023817
SSID ssj0002124274
Score 2.253908
Snippet This note introduces the concept of $ (h_1, h_2) $-convex stochastic processes using interval-valued functions. First we develop Hermite-Hadmard $...
SourceID doaj
crossref
SourceType Open Website
Enrichment Source
Index Database
StartPage 19913
SubjectTerms hermite-hadamard inequality
interval valued functions
jensen inequality
ostrowski inequality
stochastic process
Title Some well known inequalities for $ (h_1, h_2) $-convex stochastic process via interval set inclusion relation
URI https://doaj.org/article/413812d4e4ad4f3cb4a75fd3ff9557e7
Volume 8
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8QwEA7iSQ_iE9cXOSyiYNluk7bJUcVlEdaLLngrySRhF_bFPsSf70zbXfYiXjy2hDadTDLfTGe-YaypwGqXtV3kMyLVFgIiYxIiBLB524GQKlChcO8t6_bl62f6udXqi3LCKnrgSnAtPGTRBjnppXEyCLDS5GlwIgSdprkv68jR5m05U3QG44Es0d-qSDWFFrKF-I_-PRCcoRa4W0Zoi6u_NCqdQ3ZQo0H-WM3iiO34yTHb722oVBcnbPw-HXtOITZO8a8JR1hYVUKij8sRcvImvxsU7Qc-KJJ73ozKPPJvjqAOBoZYmPmsKgbgX0PDh2WOI75z4Zd4AaMVhcv4vM6JO2X9zsvHczeqeyREgHJZRokxXsfSqcSCwy_LIUiXQYbbVCkImVUu1oBeUtvIYJ2OlUsznyNu0zaJFYgztjuZTvw54z620jttQEkhHeBOlsHoGFdZmQBx3mAPa6EVUBOIUx-LUYGOBMm4IBkXaxk32O1m-Kxizvht4BOtwGYQEV6XN1ANiloNir_U4OI_HnLJ9mhSVYTliu0u5yt_jZhjaW9K9foBLaLWiQ
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=Some+well+known+inequalities+for+%24+%28h_1%2C+h_2%29+%24-convex+stochastic+process+via+interval+set+inclusion+relation&rft.jtitle=AIMS+mathematics&rft.au=Afzal%2C+Waqar&rft.au=Abbas%2C+Mujahid&rft.au=Eldin%2C+Sayed+M.&rft.au=Khan%2C+Zareen+A.&rft.date=2023-01-01&rft.issn=2473-6988&rft.eissn=2473-6988&rft.volume=8&rft.issue=9&rft.spage=19913&rft.epage=19932&rft_id=info:doi/10.3934%2Fmath.20231015&rft.externalDBID=n%2Fa&rft.externalDocID=10_3934_math_20231015
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