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In this paper, we first prove a new parameterized identity that generates a quadrature rule family similar to Simpson’s second formula, and then we establish some new Simpson-like type inequalities for functions whose first derivatives are  s -convex in the second sense, from which we can deduce the famous38{\frac{3}{8}}-Simpson inequality. We end the article with some applications.

Parameterized Simpson-like inequalities for differential s -convex functions