In this paper, we introduce two iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of a general system of variational inequalities for continuous monotone mappings and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. First, this system of variational inequalities is proven to be equivalent to...

This paper introduces a version of the argmax continuous mapping theorem that applies to M-estimation problems in which the objective functions converge to a limiting process with multiple maximizers. The concept of the smallest maximizer of a function in the d-dimensional Skorohod space is introduced and its main properties are studied. The resulting continuous mapping theorem is applied to th...

In this paper, we introduce two general iterative methods for a certain optimization problem of which the constrained set is the common set of the solution set of the variational inequality problem for a continuous monotone mapping and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Under some control conditions, we establish the strong convergence of the propo...

Abstract thought has roots in the spatial world. Abstractions are expressed in the ways things are arranged in the world as well as the ways people talk and gesture. Mappings to the page should be better when they are congruent, that is, when the abstract concept matches the spatial one. Congruent mappings can be revealed in people’s performance and preferences. Congruence is supported here for...

0 h(y(s)) ds, t ≥ 0, mapping a function x into a function y, when the underlying function space D is endowed with the Skorohod M1 topology. We apply this integral representation with the continuous mapping theorem to establish heavy-traffic stochastic-process limits for many-server queueing models when the limit process has jumps unmatched in the converging processes, as can occur with bursty a...

Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

Weak convergence of a stochastic process defined on a function space is discussed. In doing so we explore various weak convergence results generically called functional central limit theorems or invariance principles. Emphasis is placed on how to apply those theorems to deal with statistics arising from nonstationary linear time series models. It turns out that, in most cases, the continuous ma...

Two invertible dynamical systems (X,A, μ, T ) and (Y,B, ν, S) where X, Y are metrizable spaces and T , S are homeomorphisms on X and Y , are said to be finitarily orbit equivalent if there exists an invertible measure preserving mapping φ from a subset X0 of X of full measure to a subset Y0 of Y of full measure such that φ|X0 is continuous in the relative topology on X0, φ|Y0 is continuous in t...