Hadamard-type inequalities for \(s\)-convex functions. I. (English) Zbl 1226.26015

Summary: We give a refined upper bound for unit, or smaller, intervals and refinement of the Hermite-Hadamard inequality for \(s\)-convex functions in the second sense. We also establish several Hadamard-type inequalities for differentiable and twice differentiable functions based on concavity and \(s\)-convexity with applications for some special means.


26D15 Inequalities for sums, series and integrals
26E60 Means