Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions

Fangfang Shi, Guoju Ye, Dafang Zhao and Wei Liu
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Fangfang Shi: College of Science, Hohai University, Nanjing 210098, China
Guoju Ye: College of Science, Hohai University, Nanjing 210098, China
Dafang Zhao: School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
Wei Liu: College of Science, Hohai University, Nanjing 210098, China

Mathematics, 2020, vol. 8, issue 4, 1-10

Abstract: In this paper, firstly we prove the relationship between interval h -convex functions and interval harmonically h -convex functions. Secondly, several new Hermite–Hadamard type inequalities for interval h -convex functions via interval Riemann–Liouville type fractional integrals are established. Finally, we obtain some new fractional Hadamard–Hermite type inequalities for interval harmonically h -convex functions by using the above relationship. Also we discuss the importance of our results and some special cases. Our results extend and improve some previously known results.

Keywords: Hermite–Hadamard type inequalities; interval-valued functions; fractional integrals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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