On some dynamic inequalities of Ostrowski, trapezoid, and Grüss type on time scales

Abstract

Abstract In the present manuscript, we prove some new extensions of the dynamic Ostrowski inequality and its companion inequalities on an arbitrary time scale by using two parameters for functions whose second delta derivatives are bounded. In addition to these generalizations, some integral and discrete inequalities are obtained as special cases of main results.

Keywords

• Montgomery identity
• Ostrowski-type inequality
• Trapezoid-type inequality
• Grüss-type inequality
• Time scales