Local fractional integrals involving generalized strongly m-convex mappings

Abstract

In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets $${\mathbb {R}}^{\alpha }\, (0<\alpha \le 1)$$ of real line numbers. Then, using twice local fractional differentiable mappings that are in absolute value at certain powers generalized strongly m-convex, we obtain some new estimates on generalization of trapezium-like inequalities. We also discuss some new special cases which can be deduced from our main results.