Abstract
We introduce a new class of interval-valued preinvex functions termed as harmonically h-preinvex interval-valued functions. We establish new inclusion of Hermite–Hadamard for harmonically h-preinvex interval-valued function via interval-valued Riemann–Liouville fractional integrals. Further, we prove fractional Hermite–Hadamard-type inclusions for the product of two harmonically h-preinvex interval-valued functions. In this way, these findings include several well-known results and newly obtained results of the existing literature as special cases. Moreover, applications of the main results are demonstrated by presenting some examples.
Highlights
After illustrating the concept of interval-valued functions, this paper proposes a new definition of harmonically h-preinvex interval-valued functions
From the definition of harmonically h-preinvex interval-valued function, we can see that every harmonical hconvex interval-valued function is harmonically h-preinvex interval-valued function with respect to η (v, u) = v − u
We have introduced harmonically h-preinvex interval-valued functions which include harmonical h-convex interval-valued functions and harmonical convex interval-valued functions as special cases
Summary
A useful generalization of convex functions is introduced by Hanson [7] which is called invex functions. In 1986, Ben-Israel and Mond [8] proposed the notion of preinvex functions and showed that every differentiable preinvex function is invex, but the converse may not be true. Moore [10] was the first to propose the concept of interval analysis and extend the arithmetic of intervals to the computer. Provided a methodology to determine the efficient solution of general multi-objective interval fractional programming problem. Li et al [14] introduced the concept of invexity using gH-derivative of interval-valued functions and derived Kuhn–Tucker optimality conditions for an interval-valued objective function.
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