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 asymptotic group of symmetries at null infinity of flat spacetimes in three and four dimensions is the infinite dimensional Bondi-Metzner-Sachs (BMS) group. This has recently been shown to be isomorphic to non-relativistic conformal algebras in one lower dimension, the Galilean Conformal Algebra (GCA) in 2d and a closely related non-relativistic algebra in 3d [1]. We provide a better unders...

We propose an approach to analyze the asymptotic behavior of Pólya urns based on the contraction method. For this a combinatorial discrete time embedding of the evolution of the composition of the urn into random rooted trees is used. A decomposition of the trees leads to a system of recursive distributional equations which capture the distributions of the numbers of balls of each color. Ideas ...

Limit laws are proven by the contraction method for random vectors of a recursive nature as they arise as parameters of combinatorial structures such as random trees or recursive algorithms, where we use the Zolotarev metric. In comparison to previous applications of this method a general transfer theorem is derived, which allows to establish a limit law on the basis of the recursive structure ...

Contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation.We consider generalizations of contractionwith respect to a norm that allow contraction to take place after small transients in time and/or amplitude. These generalized contractive systems (GCSs) are useful for seve...

in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...

‎In this work four uncertain delay differential equations of Volterra-Levin type will be considered‎. ‎Applying suitable contraction mapping and fixed point method‎, ‎the stability the studied‎. ‎It shown that solutions are bounded and‎, ‎with additional condition‎, tend to zero‎. ‎Also‎, ‎a necessary sufficient condition for asymptotic an equation presented‎.

We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance can be finite-, high-, or infinite-dimensional. A mixture point masses at zero and continuous distributions is used the prior distribution on coefficients, appropriate parameters. The optimal posterior contraction hampered by p...

If T is a bounded linear operator on Hilbert space H and V given isometry K, we present necessary sufficient conditions in order to ensure the existence of π:H→K such that πT=V*π (i.e., (π,V*) extends T). We parametrize set all solutions π this equation. show, for example, unitary U E multiplication by independent variable Mz Hardy HD2(D), there exists an isometric π:H→E⊕HD2(D) (π,(U⊕Mz)*) if o...