On Simpson's inequality and applications

Abstract

New inequalities of Simpson type and their application to quadrature formulae in Numerical Analysis are given.

Some new bounds for Simpson's rule involving special functions via harmonic h-convexity

“…The strong relationship between theory of convexity and theory of inequalities has attracted many researchers, as a result number classical inequalities which were obtained for convex functions have also been extended for other generalizations of convex functions, see [1,2,5,7,10,11,[13][14][15][16][17][18][19]22]. Inspired by the ongoing research, in this paper we consider the class of harmonic h-convex functions and obtain some new Simpson type inequalities.…”

New estimates of the remainder term in Simpson's quadrature formula for functions of bounded variation

“…This disadvantage was overcome in the result of Dragomir et al 1,2 where the following result was proved.…”

On weighted Simpson type inequalities and applications

“…Now if we assume that I n : a = x 0 < x 1 < · · · < x n = b is a partition of the interval [a, b] and f is as above, then we can approximate the integral b a f (t) dt by the Simpson's quadrature formula A S (f, I n ), having an error given by R S (f, I n ), where For some recent results which generalize, improve and extend this classic inequality (1.1), see the papers [2] - [7] and [9] - [12].…”

“…Recently, Dragomir [6], (see also the survey paper authored by Dragomir, Agarwal and Cerone [7]) has proved the following two Simpson type inequalities for functions of bounded variation: is the best possible.…”