On error estimations of Simpson's second type quadrature formula

Abstract

In this paper, we derive some error estimates of Simpson's second type quadrature formula for functions of bounded variation and Lipschitzian mappings. Also, similar error estimations for absolutely continuous functions whose first derivatives belong to Lp[?, ?] with (p < 1 ? ?) are established. Finally, with the help of the results given in this work, some Simpson's type inequalities involving special means are presented. © 2020 John Wiley & Sons, Ltd.