The objective in this article is to extend the applicability of Newton’s method for solving Banach space valued nonlinear equations. In particular, a new semi-local convergence criterion for Newton’s method (NM) based on Kantorovich theorem in Banach space is developed by application of the Heisenberg Uncertainty Principle (HUP). The convergence region given by this theorem is small in general limiting the applicability of NM. But, using HUP and the Fourier transform of the operator involved, we show that it is possible to extend the applicability of NM without additional hypotheses. This is done by enlarging the convergence region of NM and using the concept of epsilon-concentrated operator. Numerical experiments further validate our theoretical results by solving equations in case not covered before by the Newton–Kantorovich theorem.

Falls in the geriatric population are one of the most important causes of disabilities in this age group. Its consequences impose a great deal of economic burden on health and insurance systems. This study was conducted by a multidisciplinary team with the aim of evaluating the effect of visuo-spatial-motor training for the prevention of falls in older adults. The subjects consisted of 31 volunteers aged 60 to 92 years who were studied in three groups: (1) A group under standard physical training, (2) a group under visuo-spatial-motor interventions, and (3) a control group (without any intervention). The results of the study showed that visual-spatial motor exercises significantly reduced the risk of falls of the subjects.

The often reported reduction of Reaction Time (RT) by Vision Training) is successfully replicated by 81 athletes across sports. This enabled us to achieve a mean reduction of RTs for athletes eye-hand coordination of more than 10%, with high statistical significance. We explain how such an observed effect of Sensorimotor systems’ plasticity causing reduced RT can last in practice for multiple days and even weeks in subjects, via a proof of principle. Its mathematical neural model can be forced outside a previous stable (but long) RT into a state leading to reduced eye-hand coordination RT, which is, again, in a stable neural state.