PROPERTIES AND INTEGRAL INEQUALITIES INVOLVING WITH THE GENERALIZED s-TYPE PREINVEX MAPPINGS IN FRACTAL SPACE

Shuhong Yu (), Tingsong Du and Bo Yu
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Shuhong Yu: Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China
Tingsong Du: Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China†Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China
Bo Yu: Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China†Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 07, 1-28

Abstract: As a generalization of the convex mappings, the generalized s-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 s-type preinvexity. As applications, on the basis of local fractional calculus, certain inequalities in view of numerical integration, 𠜀-type special means, as well as moments of random variable, are acquired, respectively.

Keywords: Fractal Space; Generalized s-Type Preinvexity; Local Fractional Integrals (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501584

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