In this paper we study the stability properties of a delay differential equation by means of contraction mappings. The paper is motivated by a number of difficulties encountered in the study of stability by means of Liapunov’s direct method. We notice that most of these difficulties vanish when applying fixed point theory. An asymptotic stability theorem with a necessary and sufficient conditio...

We consider a variety of subtrees of various shapes lying on the fringe of a recursive tree. We prove that (under suitable normalization) the number of isomorphic images of a given fixed tree shape on the fringe of the recursive tree is asymptotically Gaussian. The parameters of the asymptotic normal distribution involve the shape functional of the given tree. The proof uses the contraction met...

We prove sufficient conditions, ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key tool is an asymptotic decomposition of contraction kernels, realized by means of increasing families of projection operators. We also use an infinite-dimensional Clark-Ocone formula, as well as a ver...

We consider distributional recursions which appear in the study of random binary search trees with monomials as toll functions. This extends classical parameters as the internal path length in binary search trees. As our main results we derive asymptotic expansions for the moments of the random variables under consideration as well as limit laws and properties of the densities of the limit dist...

The novelty of our paper is to establish results on asymptotic stability mild solutions in $p$th moment Riemann-Liouville fractional stochastic neutral differential equations (for short FSNDEs) order $\alpha \in (\frac{1}{2},1)$ using a Banach's contraction mapping principle. core point this derive the solution FSNDEs involving time-derivative by applying version variation constants formula. ar...

Excitation-contraction (E-C) coupling was investigated in rat hearts 6 wk after induction of myocardial infarction (MI) by ligation of the left coronary artery. Heart weight was increased by 74% and left ventricular end-diastolic pressure was 23 +/- 2 mmHg in MI compared with 8 +/- 2 mmHg in sham-operated controls (Sham, P < 0.001). Cell shortening was measured in voltage-clamped myocytes at 36...

Conditions for Global Asymptotic Stability (GAS) of a nonlinear relaxation process realized by a Recurrent Neural Network (RNN) are provided. Existence. convergence, and robustness of such a process are analyzed. This is undertaken based upon the Contraction Mapping Theorein (CMT) and the corresponding Fixed Point Iteration (FPI). Upper bounds for such a process are shown to be the conditions o...

It is proved that in an idealized uniform probabilistic model the cost of a partial match query in a multidimensional quadtree after normalization converges in distribution. The limiting distribution is given as a fixed point of a random affine operator. Also a first-order asymptotic expansion for the variance of the cost is derived and results on exponential moments are given. The analysis is ...

Conditions for Global Asymptotic Stability (GAS) of a nonlinear relaxation equation realised by a Nonlinear Autoregressive Moving Average (NARMA) recurrent perceptron are provided. Convergence is derived through Fixed Point Iteration (FPI) techniques, based upon a contraction mapping feature of a nonlinear activation function of a neuron. Furthermore, nesting is shown to be a spatial interpreta...

Maintained reduction in extracellular K+ concentrations [( K]e) of isolated canine mesenteric arteries produced two contractions separated by a period of several hours. The mechanisms for respective early and late contractions were investigated. First, early responses to reduced [K]e were examined quantitatively over a period of 2 hr. Critical [K]e for initiating the contraction was 0.14 mM. Ea...