A Main Class of Integral Inequalities with Applications

Abstract

In this paper, we define some integral transforms and obtain suitable bounds for them in order to introduce a main class of integral inequalities including Ostrowski and Ostrowski-Gr¨uss inequalities and various kinds of new integral inequalities. In this sense, we also introduce a three point quadrature formula and obtain its error bounds.

Keywords

• Ostrowski inequality
• Ostrowski-Gr¨uss inequality
• integral transforms
• error bounds
• quadrature rules