Abstract
First, we define what we named the generalized [Formula: see text]-polynomial convex mappings as a generalization of convex mappings, investigate their meaningful properties, and establish two Hermite–Hadamard’s-type integral inequalities via the newly proposed mappings in the frame of fractal space as well. Second, in accordance with the discovered identity with a parameter, we present certain improved integral inequalities with regard to the mappings whose first-order derivatives in absolute value belong to the generalized [Formula: see text]-polynomial convexity. As applications, on the basis of local fractional calculus, we acquire three inequalities in view of special means, numerical integrations, as well as probability density mappings, respectively.
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