Quantum Estimates for Different Type Intequalities through Generalized Convexity

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(-).

Automated summary

This article extends several integral inequalities involving (h-m)-convexity via quantum calculus, generalizes some quantum integral inequalities for q-differentiable (h-m)-convexity, and can serve as the refinement and unification of classical results in the literature by taking the limit q -> 1(-).