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

Abstract

The fractal [Formula: see text]-preinvex mappings are put forward and their properties are investigated firstly. Meanwhile, some fractal Hermite–Hadamard-type ([Formula: see text]) and Fejér–Hermite–Hadamard-type ([Formula: see text]) inequalities concerning [Formula: see text]-preinvexity are popularized. Then, two weighted parameterized [Formula: see text]-fractal identities are proposed, which involve twice the local fractional differentiable mappings. Based upon these identities and taking advantage of the fractal [Formula: see text]-preinvex mappings as well as [Formula: see text]-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.