Parameterized Simpson-like inequalities for differential s-convex functions

Abstract

Abstract 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 famous 3 8 {\frac{3}{8}} -Simpson inequality. We end the article with some applications.