We prove the Lipschitz dependence on the initial condition of the solution set of a nonconvex second-order differential inclusions by applying the contraction principle in the space of selections of the multifunction instead of the space of solutions.

In this paper, the existence and uniqueness of the solution of random impulsive neutral functional differential equation is investigated under sufficient condition. The results are obtained by using the Contraction principle.

This letter presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of Neural Contraction Metric (NCM). The NCM uses long short-term memory recurrent neural network global approximation an optimal contraction metric, existence which is necessary sufficient condition exponential stability systems. optimality stems from fact that metrics sampled ...

We have investigated the existence and uniqueness solutions of the nonlinear fractional differential equation of an arbitrary order with integral boundary condition. The result is an application of the Schauder fixed point theorem and the Banach contraction principle.

The existence of coincidence points and common fixed points for operators satisfying a Presić-Kannan type contraction condition in a metric spaces setting is proved. A multi-step iterative method for constructing the common fixed points is also provided.

In this paper, we extend and improve the condition of contraction of results of Azam et al. for two single-valued mappings on a closed ball in complex valued metric spaces.

Capsular contraction following implantation of breast prostheses occurs in 2-33% of patients undergoing breast augmentation. This condition can be debilitating for patients, and often requires revisional surgery. The aetiology of capsular contraction is unclear, but may be due to infection, haematoma or foreign body-type reactions.Methylene blue dye is a substance known to cause localised tissu...

Array contraction is an optimization that transforms array variables into scalar variables within a loop. While the opposite transformation, scalar expansion, is used for enabling parallelism (with a penalty in memory size), array contraction is used to save memory by removing temporary arrays and to increase locality. Several heuristics have already been proposed to perform array contraction t...

Random fixed point theorems for condensing 1-set contraction selfmaps are known. But no random fixed point theorem for more general asymptotic 1-set contraction selfmaps is yet available. The purpose of this paper is to prove random fixed point theorems for such maps. 1. Introduction. Random fixed point theorems are stochastic versions of (classical or deterministic) fixed point theorems and ar...

The aim of this study was to investigate the difference in a muscle contraction phase dependence between ipsilateral (ipsi)- and contralateral (contra)-primary motor cortex (M1) excitability during repetitive isometric contractions of unilateral index finger abduction using a transcranial magnetic stimulation (TMS) technique. Ten healthy right-handed subjects participated in this study. We inst...