Hermite–Hadamard-type inequalities for strongly $$(\alpha ,m)$$ -convex functions via quantum calculus

Abstract

In this paper, we derive a quantum analogue of Hermite–Hadamard-type inequalities for twice differentiable convex functions whose second derivatives in absolute value are strongly \((\alpha ,m )\)-convex. We obtain new bounds using the H\(\ddot{o}\)lder and power mean inequalities. Moreover, we provide suitable examples in support of our theoretical results. We correlate our findings with comparable results in the literature and show that the obtained results are refinements and improvements.