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

Mathematics

Wei Liu¹  Fangfang Shi¹  Guoju Ye¹  Dafang Zhao² 

[1] College of Science, Hohai University, Nanjing 210098, China;School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China;

关键词: Hermite–Hadamard type inequalities;    interval-valued functions;    fractional integrals;   

DOI  :  10.3390/math8040534

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown