Mathematica Eterna
Open Access

Abstract

Some estimates on the Simpson’s type inequalities through s-convex and quasi-convex stochastic processes

Jes´us Materano,Nelson Merentes and Maira Valera-L´opez

We obtain several inequalities of Simpson’s type by giving explicit error bounds in the Simpson’s rules, by means of Peano type kernels and results from the modern theory of inequalities. A midpoint type inequalities are given. The approach presented here using s-convex and quasi-convex stochastic processes in terms of up to second derivatives are obtained for first time.