THE LAPUNOV METHOD AS A SPECIAL CASE OF THE BANACH CONTRACTION MAPPING-THEOREM

The Banach contraction mapping theorem has provided the basis for many analyses in various fields of technology, particularly where the goal was to prove the existence and uniqueness of the solution. The Lapunov theorem has also been the basis for analyses of technical systems as well as for stability evaluation. The purpose of the present work is to demonstrate that the Lapunov theorem is in its essence a particular case of the Banach contraction-mapping theorem. This conclusion is based on the observation that every Lapunov function can be used to define a distance.