The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and Hölder’s inequality, some new Simpson type for the product of strongly extended s-convex function are ...

Our aim in this article is to incorporate the notion of "strongly s-convex function" and prove a new integral identity. Some new inequalities of Simpson type for strongly s-convex function utilizing integral identity and Holder's inequality are considered.

In this paper, we generalize Cerone’s results, and a unified treatment of error estimates for a general inequality satisfying f (n−1) being of bounded variation is presented. We derive the estimates for the remainder terms of the mid-point, trapezoid, and Simpson formulas. All constants of the errors are sharp. Applications in numerical integration are also given. c © 2007 Elsevier Ltd. All rig...

A large body of survey research offers evidence that citizens are not always fully aware of the economic and political realities in their respective countries. Norton and Ariely (2011) extended this research to the domain of wealth inequality, showing that Americans were surprisingly unaware of the shape of the wealth distribution in America. Using an alternative methodology, Eriksson and Simps...

Abstract In this paper, based on a given parameterized identity that generates quadrature rule family similar to Simpson’s second formula, we establish some new Simpson-like type inequalities for functions with bounded as well Lipchitzian derivatives from which can deduce the famous 3 / 8-Simpson’s inequality. The study concludes an application example management science.

Abstract In this paper, we offer a new quantum integral identity, the result is then used to obtain some estimates of Hermite–Hadamard inequalities for integrals. The results presented in paper are generalizations comparable literature on inequalities. Several inequalities, such as midpoint-like inequality, Simpson-like averaged midpoint–trapezoid-like and trapezoid-like obtained special cases ...