PROPERTIES AND 2α̃-FRACTAL WEIGHTED PARAMETRIC INEQUALITIES FOR THE FRACTAL (m,h)-PREINVEX MAPPINGS

Xiaohua Zhang (), Yunxiu Zhou () and Tingsong Du
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Xiaohua Zhang: School of Mathematics, Yunnan Normal University, Kunming 650500, Yunnan, P. R. China
Yunxiu Zhou: Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, Hubei, P. R. China
Tingsong Du: Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, Hubei, P. R. China†Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, Hubei, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 09, 1-36

Abstract: The fractal (m,h)-preinvex mappings are put forward and their properties are investigated firstly. Meanwhile, some fractal Hermite–Hadamard-type (HH) and Fejér–Hermite–Hadamard-type (FHH) inequalities concerning (m,h)-preinvexity are popularized. Then, two weighted parameterized 2α̃-fractal identities are proposed, which involve twice the local fractional differentiable mappings. Based upon these identities and taking advantage of the fractal (m,h)-preinvex mappings as well as (φ,Ï Î±Ìƒ)-Lipschitzian mappings, a range of error estimations are deduced in the fractal domains. Finally, certain fractal inequalities with relation to the weighted formula and random variable are correspondingly presented as applications.

Keywords: Fractal (m; h)-Preinvex Mappings; Parameterized Inequality; Weighted Inequality; Local Fractional Theory (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23501347

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