PROPERTIES AND INTEGRAL INEQUALITIES ARISING FROM THE GENERALIZED n-POLYNOMIAL CONVEXITY IN THE FRAME OF FRACTAL SPACE

First, we define what we named the generalized n-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 n-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.

Automated summary

This study firstly defines the generalized n-polynomial convex mappings as a generalization of convex mappings and explores their properties. It then establishes two Hermite-Hadamard's-type integral inequalities in the frame of fractal space, as well as presents improved integral inequalities for mappings with first-order derivatives in absolute value belonging to the generalized n-polynomial convexity.