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.
Highlights
Fractional calculus [1–21] is invariably important in almost all areas of mathematics and other natural sciences
We consider the p-convex function which assumes a dynamic job in portraying the idea of the interval-valued function just as establishing several generalizations by employing the Katugampola fractional integral operator
The principal objective of this article is that we propose the notion of p-convex function for the interval-valued function
Summary
Fractional calculus [1–21] is invariably important in almost all areas of mathematics and other natural sciences. Let Q : I → R be a convex function. We consider the p-convex function which assumes a dynamic job in portraying the idea of the interval-valued function just as establishing several generalizations by employing the Katugampola fractional integral operator. We present the results concerning Hermite– Hadamard inequality, Fejér type inequality, and certain other related variants by employing p-convexity, which correlates with the Katugampola fractional integral operator.
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