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In this paper, we establish some integral inequalities of Simpson's type for (α, m)-convex functions.

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In the paper, the authors set up an identity for a function whose third derivative is integrable, establish by the Hölder inequality some new integral inequalities of the Hermite–Hadamard type for extended s-convex functions in the second sense, and apply these integral inequalities to construct inequalities for several special means.

In the paper, the authors establish a new integral identity and by this identity with the Hölder integral inequality, discover some new Hermite-Hadamard type integral inequalities for functions whose second derivatives are (α, m)-convex.