3/8-Simpson Type Inequalities for Functions whose Modulus of First Derivatives and its q-TH Powers are s-Convex in the Second Sense

Abstract

The purpose of this study is to improve certain existing results concerning the Simpson type inequalities involving four point called Simpson second formula. First, we prove a new integral identity. Then, we use this identity to come up with a new Simpson second formula inequalities for functions whose first derivatives are s-convex. We also deal with situations in which the first derivatives
are bounded and Lipschitzian. In addition, some applications are given to show how well our main results work.

Key words and phrases. 3/8-Simpson inequality, Newton-Cotes quadrature, s-convex functions, Lipschitzian functions, bounded functions.

2010 Mathematics Subject Classification. 26D10, 26D15, 26A51