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...

banach contraction principle has been generalized in different spaces by mathematicians over the years. mustafa and sims [18] proposed a new class of generalized metric spaces, which are called as g-metric spaces. in this type of spaces a non-negative real number is assigned to every triplet of elements. many mathematicians studied extensively various results on g-metric spaces by using the con...

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...

The signaling cascades initiated by motilin receptors in gastric and intestinal smooth muscle cells were characterized. Motilin bound with high affinity (IC(50) 0.7 +/- 0.2 nM) to receptors on smooth muscle cells; the receptors were rapidly internalized via G protein-coupled receptor kinase 2 (GRK2). Motilin selectively activated G(q) and G(13), stimulated G alpha(q)-dependent phosphoinositide ...

We use a semianalytic model to examine the collapse of supercritical cores (i.e., cores with a mass-toÑux ratio exceeding a critical value). Recent numerical simulations of the formation and contraction of supercritical cores show that the inner solution tends toward self-similar evolution. We use this feature to develop analytic expressions for quantities such as the density, angular velocity,...

Just as O-notation provides an asymptotic upper bound on a function, Ω-notation provides an asymptotic lower bound. In other words, Ω-notation is the asymptotic equivalent of “≥”. For a given function g(n), we denote by Ω(g(n)) (pronounced “big omega of g of n” or sometimes just “omega of g of n”) the set of all functions f(n), such that there exist positive constants c and n0 such that 0 ≤ cg(...