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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Bibliographic Details
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
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-021-02623-w