Abstract
This article estimates several integral inequalities involving
(
h
−
m
)
-convexity via the quantum calculus, through which Important integral inequalities including Simpson-like, midpoint-like, averaged midpoint-trapezoid-like and trapezoid-like are extended. We generalized some quantum integral inequalities for q-differentiable
(
h
−
m
)
-convexity. Our results could serve as the refinement and the unification of some classical results existing in the literature by taking the limit
q
→
1
−
.