Generalization of Montgomery identity via Taylor formula on time scales

Abstract

Abstract In the current paper, a generalized Montgomery identity is obtained with the help of Taylor’s formula on time scales. The obtained identity is used to establish Ostrowski inequality, mid-point inequality, and trapezoid inequality. Moreover, the weighted versions of generalized Montgomery identity and respective Ostrowski inequality are also discussed. Special cases are obtained for different time scales to obtain new and existing results.

Keywords

• Montgomery identity
• Ostrowski inequality
• Trapezoid inequality
• Time scales calculus