Hermite–Hadamard-type inequalities for interval-valued preinvex functions via Riemann–Liouville fractional integrals

In this paper, we introduce ( h 1 , h 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two inter...

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Published inJournal of inequalities and applications Vol. 2021; no. 1; pp. 1 - 15
Main Authors Sharma, Nidhi, Singh, Sanjeev Kumar, Mishra, Shashi Kant, Hamdi, Abdelouahed
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2021
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Fractional calculus
Fractional integrals
Hermite–Hadamard inequalities
Inequalities
Integrals
Interval-valued functions
Invex sets
Mathematics
Mathematics and Statistics
Preinvex functions
28B20
Preinvex functions
Interval-valued functions
26A51
Hermite–Hadamard inequalities
26A33
Invex sets
Fractional integrals
26E25
26D15
Online AccessGet full text

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Abstract In this paper, we introduce ( h 1 , h 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two interval-valued functions. Further, some examples are given to confirm our theoretical results.
AbstractList Abstract In this paper, we introduce ( h 1 , h 2 ) $(h_{1},h_{2})$ -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two interval-valued functions. Further, some examples are given to confirm our theoretical results.
In this paper, we introduce (h1,h2)-preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two interval-valued functions. Further, some examples are given to confirm our theoretical results.
In this paper, we introduce $(h_{1},h_{2})$ ( h 1 , h 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two interval-valued functions. Further, some examples are given to confirm our theoretical results.
In this paper, we introduce ( h 1 , h 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two interval-valued functions. Further, some examples are given to confirm our theoretical results.
ArticleNumber 98
Author Hamdi, Abdelouahed
Mishra, Shashi Kant
Sharma, Nidhi
Singh, Sanjeev Kumar
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  surname: Sharma
  fullname: Sharma, Nidhi
  organization: Department of Mathematics, Institute of Science, Banaras Hindu University
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  givenname: Sanjeev Kumar
  surname: Singh
  fullname: Singh, Sanjeev Kumar
  organization: Department of Mathematics, Institute of Science, Banaras Hindu University
– sequence: 3
  givenname: Shashi Kant
  surname: Mishra
  fullname: Mishra, Shashi Kant
  organization: Department of Mathematics, Institute of Science, Banaras Hindu University
– sequence: 4
  givenname: Abdelouahed
  orcidid: 0000-0003-1950-8907
  surname: Hamdi
  fullname: Hamdi, Abdelouahed
  email: abhamdi@qu.edu.qa
  organization: Department of Mathematics, Statistics and Physics College of Arts and Sciences, Qatar University
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Keywords 28B20
Preinvex functions
Interval-valued functions
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Hermite–Hadamard inequalities
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Invex sets
Fractional integrals
26E25
26D15
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References_xml – reference: TunçT.SarikayaM.Z.SrivastavaH.M.Some generalized Steffensen’s inequalities via a new identity for local fractional integralsInt. J. Anal. Appl.2017131981071378.26023
– reference: BhurjeeA.K.PandaG.Efficient solution of interval optimization problemMath. Methods Oper. Res.2012763273288300098710.1007/s00186-012-0399-0
– reference: Işcan, I.: Hermite-Hadamard’s inequalities for preinvex functions via fractional integrals and related fractional inequalities (2012) arXiv:1204.0272
– reference: BhurjeeA.K.PandaG.Multi-objective interval fractional programming problems: an approach for obtaining efficient solutionsOpsearch2015521156167332038010.1007/s12597-014-0175-4
– reference: MooreR.E.KearfottR.B.CloudM.J.Introduction to Interval Analysis2009PhiladelphiaSIAM10.1137/1.9780898717716
– reference: SrivastavaH.M.TsengK.-L.TsengS.-J.LoJ.-C.Some generalization of Maroni’s inequality on time scalesMath. Inequal. Appl.201114246948028153331217.26069
– reference: MohanS.R.NeogyS.K.On invex sets and preinvex functionsJ. Math. Anal. Appl.19951893901908131255910.1006/jmaa.1995.1057
– reference: MooreR.E.Methods and Applications of Interval Analysis1979PhiladelphiaSIAM10.1137/1.9781611970906
– reference: WeiW.SrivastavaH.M.ZhangY.WangL.ShanP.ZhangT.A local fractional integral inequality on fractal space analogous to Anderson’s inequalityAbstr. Appl. Anal.20142014324056307023094
– reference: LupulescuV.Fractional calculus for interval-valued functionsFuzzy Sets Syst.20152656385331032710.1016/j.fss.2014.04.005
– reference: LupulescuV.Hukuhara differentiability of interval-valued functions and interval differential equations on time scalesInf. Sci.20132485067309583510.1016/j.ins.2013.06.004
– reference: WeirT.MondB.Preinvex functions in multiple objective optimizationJ. Math. Anal. Appl.1988136293897258110.1016/0022-247X(88)90113-8
– reference: HansonM.A.On sufficiency of the Kuhn-Tucker conditionsJ. Math. Anal. Appl.198180254555061484910.1016/0022-247X(81)90123-2
– reference: BhurjeeA.K.PandaG.Sufficient optimality conditions and duality theory for interval optimization problemAnn. Oper. Res.20162431335348352980610.1007/s10479-014-1644-0
– reference: SrivastavaH.M.TsengK.-L.TsengS.-J.LoJ.-C.Some weighted Opial type inequalities on time scalesTaiwan. J. Math.2010141107122260344510.11650/twjm/1500405730
– reference: Chalco-CanoY.LodwickW.A.Condori-EquiceW.Ostrowski type inequalities and applications in numerical integration for interval-valued functionsSoft Comput.201519113293330010.1007/s00500-014-1483-6
– reference: WangJ.FečkanM.Fractional Hermite-Hadamard Inequalities2018Berlinde Gruyter10.1515/9783110523621
– reference: RoyP.PandaG.Expansion of generalized Hukuhara differentiable interval-valued functionNew Math. Nat. Comput.201915355357010.1142/S1793005719500327
– reference: SharmaN.MishraS.K.HamdiA.A weighted version of Hermite-Hadamard type inequalities for strongly GA-convex functionsInt. J. Adv. Appl. Sci.20207311311810.21833/ijaas.2020.03.012
– reference: HilgerS.Ein Makettenkalkl mit anwendung auf zentrumsmannigfaltigkeiten1988WurzburgUniverstat Wurzburg0695.34001
– reference: MishraS.K.SharmaN.On strongly generalized convex functions of higher orderMath. Inequal. Appl.201922111112139059741416.26023
– reference: BudakH.TunçT.SarikayaM.Z.Fractional Hermite-Hadamard-type inequalities for interval-valued functionsProc. Am. Math. Soc.20191482705718405220810.1090/proc/14741
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Snippet In this paper, we introduce ( h 1 , h 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued...
In this paper, we introduce $(h_{1},h_{2})$ ( h 1 , h 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex...
In this paper, we introduce (h1,h2)-preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by...
Abstract In this paper, we introduce ( h 1 , h 2 ) $(h_{1},h_{2})$ -preinvex interval-valued function and establish the Hermite–Hadamard inequality for...
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SubjectTerms Analysis
Applications of Mathematics
Fractional calculus
Fractional integrals
Hermite–Hadamard inequalities
Inequalities
Integrals
Interval-valued functions
Invex sets
Mathematics
Mathematics and Statistics
Preinvex functions
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Title Hermite–Hadamard-type inequalities for interval-valued preinvex functions via Riemann–Liouville fractional integrals
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