Abstract
In this paper, we introduce the concepts of map mathcal {T} and interval-valued mathcal {T}-convex, and give some basic properties. Further, we extend fractional Hermite–Hadamard inequalities in the case of mathcal {T}-convex and Ostrowski type inequalities for interval-valued functions. Several examples are presented to illustrate the results.
Highlights
Interval analysis was first proposed in order to reduce errors during mathematical computation
In 2015, Lupulescu developed a theory of the fractional calculus for interval-valued functions in [11]
In 2019, ChalcoCano dealt with the algebra of gH-differentiable interval-valued functions in [5]
Summary
Interval analysis was first proposed in order to reduce errors during mathematical computation. In 2015, Lupulescu developed a theory of the fractional calculus for interval-valued functions in [11]. (2020) 2020:544 work of Lupulescu, in 2019, Budak and Tunç presented the right-hand side Riemann– Liouville fractional integral for interval-valued functions and studied fractional Hermite– Hadamard inequalities. Motivated by the above works, we define a map T and introduce the concept of T -convex interval-valued functions in this paper.
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