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

摘要

The fractal (m,h)-preinvex mappings are put forward and their properties are investigated firstly. Meanwhile, some fractal Hermite-Hadamard-type (HH) and Fejer-Hermite-Hadamard-type (FHH) inequalities concerning (m,h)-preinvexity are popularized. Then, two weighted parameterized 2 alpha-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 (phi,rho(alpha))-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.

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