期刊
出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218348X22500840
关键词
Generalized n-Polynomial Convex Mappings; Local Fractional Integrals; Hermite-Hadamard's Inequalities
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.
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.
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