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Certain Hadamard Proportional Fractional Integral Inequalities
Open AccessArticle

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

1
College of Science, Hohai University, Nanjing 210098, China
2
School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 534; https://doi.org/10.3390/math8040534
Received: 6 February 2020 / Revised: 21 March 2020 / Accepted: 22 March 2020 / Published: 4 April 2020
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. View Full-Text
Keywords: Hermite–Hadamard type inequalities; interval-valued functions; fractional integrals Hermite–Hadamard type inequalities; interval-valued functions; fractional integrals
MDPI and ACS Style

Shi, F.; Ye, G.; Zhao, D.; Liu, W. Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions. Mathematics 2020, 8, 534.

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