Generalization of Montgomery identity via Taylor formula on time scales

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.

New Diamond-α Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces

“…In particular, for a survey on classical inequalities on time scales, see [16], and for Riemann and Lebesgue integration on time scales, see [17]. Some other recent approaches in time scale calculus can be found in papers [18][19][20][21]. Further, for an overview of recent developments of multivariable time scale calculus, we refer the reader to [22].…”