@article{article_1676518, title={Existence and approximation for nonlinear dynamic equations using monotone iteration method}, journal={Hitit Journal Of Science}, volume={2}, pages={31–36}, year={2025}, author={Alsharif, Nour}, keywords={Comparison results, Monotone iterative technique, Coupled upper and lower solutions}, abstract={This paper improves a generalized monotone iterative technique for solving dynamic initial value problems (IVPs) on time scales, using the method of coupled lower and upper solutions. We construct monotone sequences of iterates, each of which corresponds to a solution of the dynamic IVP on time scales. Under suitable conditions, we establish the uniform and monotonic convergence of sequences to the extremal (minimal and maximal) solutions of the problem. The results provide a unified framework for analyzing dynamic equations on time scales via monotone iteration.}, number={2}, publisher={Hitit University}