We prove a limit theorem for the total Steiner k-distance of a random b-ary recursive tree with weighted edges. The total Steiner k-distance is the sum of all Steiner k-distances in a tree and it generalises the Wiener index. The limit theorem is obtained by using a limit theorem in the general setting of the contraction method. In order to use the contraction method we prove a recursion formul...

Let T be a periodic time scale. We use a fixed point theorem due to Krasnoselskii to show that the nonlinear neutral dynamic equation with infinite delay x(t) = −a(t)x(t) + (Q(t, x(t− g(t))))) + ∫ t −∞ D (t, u) f (x(u)) ∆u, t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the...

Let T be a periodic time scale. We use a fixed point theorem due to Krasnosel’skĭı to show that the nonlinear neutral dynamic equation with delay x(t) = −a(t)x(t) + (Q(t, x(t), x(t− g(t))))) +G ` t, x(t), x(t− g(t)) ́ , t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the aid ...

By introducing a new concept called “set-valued asymptotic contraction of final type” in metric spaces, the existence and uniqueness of compact fixed sets for such mappings have been obtained. Furthermore, by adding additional conditions, we prove the existence and uniqueness of endpoints for these maps. 2010 Mathematics Subject Classification: 47H10; 54C60

The paper is concerned with the asymptotic behavior of solutions to a second order nonlinear differential equation u′′ + f (t, u) = 0. Using the Banach contraction principle, we establish global existence of solutions which satisfy u(t) = At + o(tν) as t→ +∞, where A ∈ R and ν ∈ (0, 1].

The non-linear evolution of a stratified perturbation in a three dimensional expanding Universe is considered. A general Lagrangian scheme (Q model) is introduced and numerical investigations are performed. The asymptotic contraction of the core of the agglomeration is studied. A power-law scaling is detected and an heuristic interpretation of the numerical findings is provided. An asymptotic e...

This paper proves exponential asymptotic stability of discrete-time filters for the estimation of solutions to stochastic difference equations, when the observation noise is bounded. No assumption is made on the ergodicity of the signal. The proof uses the Hilbert projective metric, introduced into filter stability analysis by Atar and Zeitouni [1], [2]. It is shown that when the signal noise i...

The method of making Monte Carlo calculations of the velocity of fast axonal transport is described and applied in a relatively simple case. These illustrative calculations are supplemented by a differential equation solution of the same problem, valid as an asymptotic limit. The latter treatment is closely related to the theory of muscle contraction.

The contraction method for recursive algorithms is extended to the multivariate analysis of vectors of parameters of recursive structures and algorithms. We prove a general multivariate limit law which also leads to an approach to asymptotic covariances and correlations of the parameters. As an application the asymptotic correlations and a bivariate limit law for the number of key comparisons a...

Important problems in wireless networks can often be solved by computing fixed points of standard or contractive interference mappings, and the conventional fixed point algorithm is widely used for this purpose. Knowing that the mapping used in the algorithm is not only standard but also contractive (or only contractive) is valuable information because we obtain a guarantee of geometric converg...