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

Advances in Difference Equations

Thabet Abdeljawad¹  Saima Rashid²  Yu-Ming Chu³  Hasib Khan⁴ 

[1] Department of Mathematics and General Sciences, Prince Sultan University;Department of Mathematics, Government College (GC) University;Department of Mathematics, Huzhou University;Department of Mathematics, Shaheed Benazir Bhutto University;

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

DOI  :  10.1186/s13662-020-02782-y

来源: DOAJ

【 摘 要 】

Abstract 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】

Unknown