Abstract
As a generalization of the convex mappings, the generalized [Formula: see text]-type preinvex mappings are firstly introduced. Their meaningful properties are then investigated and the Hermite–Hadamard-type integral inequalities via the newly proposed mappings in fractal space are developed. In accordance with the newly proposed identity with three parameters, it is interesting to present certain integral inequalities with regard to the mappings whose first-order derivatives in absolute value belong to the generalized [Formula: see text]-type preinvexity. As applications, on the basis of local fractional calculus, certain inequalities in view of numerical integration, [Formula: see text]-type special means, as well as moments of random variable, are acquired, respectively.
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