International Monthly Seminar on Time Scales Analysis

In this talk, we shall investigate the validity of the Wirtinger inequality within the framework of time scales, a unified approach to continuous and discrete analysis. By constructing explicit counterexamples, we demonstrate that the classical Wirtinger inequality does not hold universally across all time scales. Motivated by this finding, we propose a reformulation of the inequality by modifying its underlying conditions. Additionally, we establish several new improved Wirtinger-like inequalities, extending the theoretical foundation of the inequality on time scales.