Quantum Estimates for Different Type Intequalities through Generalized Convexity

This article estimates several integral inequalities involving [Formula: see text]-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 [Formula: see text]-convexity. Our results could serve as the refinement and the unification of some classical results existing in the literature by taking the limit [Formula: see text].