An analogue of the Ostrowski inequality and applications

Abstract

A new analogue of the Ostrowski inequality is introduced in three different cases for functions in L1[a; b] and L?[a; b] spaces and its application is given for deriving error bounds of some quadrature rules.

Generalized Ostrowski inequalities and computational integration

“…Remark 2.15. The inequality established in (2.18) is the special case of Theorem 3 presented in [13] and [14].…”

“…Remark 2.12. The inequality (2.14) represents the generalized case of Theorem 2 presented in [13] and [14].…”

“…Also explicit error bounds for numerical quadrature and nonstandard quadrature formulas will be discussed. Also we recaptured many established results from articles [12], [13], [14] and [21].…”

A Main Class of Integral Inequalities With Applications

“…Following the papers of Masjed-Jamei and Dragomir [9,10,11,12,13], let us introduce the integral transform L K (. ; x) as follows.…”

On the Ostrowski-Gr\"{u}ss-Like Type Inequality and an Analogue of Ostrowski-Like Type Inequality

“…In [6], Masjed-Jamei and Dragomir introduced a new analogue of the Ostrowski type inequality in three different cases and apply them for some quadrature rules and proved the following theorem:…”