First, we introduce a generalized [Formula: see text]-convexity concept defined on the real linear fractal set [Formula: see text] [Formula: see text] and discuss the relation between generalized [Formula: see text]-convexity and [Formula: see text]-convexity. Second, we present several important properties of the generalized [Formula: see text]-convex mappings. Meanwhile, via local fractional integrals, we also derive certain estimation-type results on generalizations of Hadamard-type, Fejér-type and Simpson-type inequalities. As applications related to local fractional integrals, we construct several inequalities for generalized probability density mappings and [Formula: see text]-type special means.
No takes yet. Share an insight, caveat, or question.
Du et al. (2019) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: