On new fractional integral inequalities for p -convexity within interval-valued functions

Advances in Difference Equations

article

Abdeljawad, Thabet¹  Rashid, Saima⁴  Khan, Hasib⁵  Chu, Yu-Ming⁶ 

[1] Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University;Department of Computer Science and Information Engineering, Asia University;Department of Mathematics, Government College (GC) University;Department of Mathematics, Shaheed Benazir Bhutto University;Department of Mathematics, Huzhou University;Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology

关键词: p -convexity;    Katugampola fractional integral operator;    Interval-valued function;    Hermite–Hadamard inequality;   

DOI  :  10.1186/s13662-020-02782-y

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This work mainly investigates a class of convex interval-valued functions via the Katugampola fractional integral operator. By considering the p-convexity of the interval-valued functions, we establish some integral inequalities of the Hermite–Hadamard type and Hermite–Hadamard–Fejér type as well as some product inequalities via the Katugampola fractional integral operator. In addition, we compare our results with the results given in the literature. Applications of the main results are illustrated by using examples. These results may open a new avenue for modeling, optimization problems, and fuzzy interval-valued functions that involve both discrete and continuous variables at the same time.

【 授权许可】

CC BY