DIAMOND OSTROWSKI TYPE INEQUALITIES ON TIME SCALES

Abstract

This article explores Ostrowski-type inequalities within the framework of time scales, empowering the theory of Diamond-  derivatives. The study establishes the validity of these inequalities in both nabla and delta calculus, highlighting a unified approach applicable to arbitrary dynamic time scales. Furthermore, it extends these results to enclose specialized inequalities as unique cases for specific time scales, such as  and . These findings not only bridge discrete and continuous analyses but also upgrade the mathematical tools for dynamic systems on generalized time scales, offering broad applications in pure and applied mathematics.