Two different sufficient conditions are given for the convergence of the Magnus expansion arising in the study of the linear differential equation Y ′ = A(t)Y . The first one provides a bound on the convergence domain based on the norm of the operator A(t). The second condition links the convergence of the expansion with the structure of the spectrum of Y (t), thus yielding a more precise chara...

This paper investigates the rate of convergence of an alternative approximation method for stochastic differential equations. The rates of convergence of the one-step and multi-step approximation errors are proved to be O((∆t)2) and O(∆t) in the Lp sense respectively, where ∆t is discrete time interval. The rate of convergence of the one-step approximation error is improved as compared with met...

in this paper, we prove the existence of fixed point for j-type multi-valuedmap t in cat(0) spaces and also we prove the strong convergence theoremsfor ishikawa iteration scheme without using the xed point of involving map.

This article presents an innovative methodology to empirically evaluate the response of the rate of convergence in the neoclassical growth model to changes in the conditional factors. We apply this method to test the sensitivity of the speed of convergence in the EU-15 during the period 1980-2002 to increases in human and public capital. INTRODUCTION The relation between private productivity an...

We consider functions F : R n ! R n which are homogeneous and nonexpansive in thè 1 norm. We refer to these as topical functions. We study the existence of the cycle time vector (F) = lim k!1 F k (~ x)=k, which, if it exists, is independent of ~ x 2 R n. For a restricted class of topical functions, the cycle time is known to be implicated in the existence of xed points and this provides the mot...

In the paper we show equivalence of the convergence of filters on a topological space and the convergence of nets in the space. We also give, five characterizations of compactness. Namely, for any topological space T we proved that following condition are equivalent: • T is compact, • every ultrafilter on T is convergent, • every proper filter on T has cluster point, • every net in T has cluste...

in this paper, the multistage variational iteration method is implemented to solve a general form of the system of first-order differential equations. the convergence of the proposed method is given. to illustrate the proposed method, it is applied to a model for hiv infection of cd4+ t cells and the numerical results are compared with those of a recently proposed method.

Let (Ω,F , μ) be a probability space and let T = P1P2 · · ·Pd be a finite product of conditional expectations with respect to the sub σ-algebras F1,F2, . . . ,Fd. Since conditional expectations are contractions of all Lp(μ) spaces, p ∈ [1,∞], so is T . When d = 2, Burkholder and Chow [2] proved that for every f ∈ L2(μ) the iterates T f converge a.s. (and thus also in L2-norm) to the conditional...

‎In this paper‎, ‎first we study the weak and strong convergence of solutions to the‎ ‎following first order nonhomogeneous gradient system‎ ‎$$begin{cases}-x'(t)=nablaphi(x(t))+f(t), text{a.e. on} (0,infty)\‎‎x(0)=x_0in Hend{cases}$$ to a critical point of $phi$‎, ‎where‎ ‎$phi$ is a $C^1$ quasi-convex function on a real Hilbert space‎ ‎$H$ with ${rm Argmin}phineqvarnothing$ and $fin L^1(0...