Almost Fixed Points and Fixed Points of Upper [Lower] Semicontinuous Multimap on Locally G-convex Spaces

In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.

The existence of generalized synchronisation of three bidirectionally coupled chaotic systems

The existence of two types of generalized synchronisation is studied. The model considered here includes three bidirectionally coupled chaotic systems, and two of them denote the driving systems, while the rest stands for the response system. Under certain conditions, the existence of generalised synchronisation can be turned to a problem of compression fixed point in the family of Lipschitz functions. In addition, theoretical proofs are proposed to the exponential attractive property of generalised synchronisation manifold. Numerical simulations validate the theory.

Fixed Points for Mean Non-expansive Mappings

For a Banach Space X Garcia-Falset introduced the coefficient R（X） and showed that if R（X） 〈 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that ｜｜Tx - TY｜｜ ≤ a｜｜x - y｜｜ ＋ b｜｜x - Ty｜｜ for any x,y E X, where a,b ≥ 0, a ＋ b ≤ 1. We show that if R（X） 〈 1/1＋b then T has a fixed point in X.

Asymptotically Isometric Copy of l~β(0<β<1) in Spacesof Bounded Linear Operators

Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.

Efficient Estimation and Variable Selection in Dynamic Panel Data Partially Linear Varying Coefficient Models with Incidental Parameter

This paper is concerned with the statistical inference of partially linear varying coefficient dynamic panel data model with incidental parameter, including efficient estimation of the parametric and nonparametric components and consistent determination of the lagged order. For the parametric component, we propose an efficient semiparametric generalized method-of-moments（GMM） estimator and establish its asymptotic normality. For the nonparametric component, B-spline series approximation is employed to estimate the unknown coefficient functions, which are shown to achieve the optimal nonparametric convergence rate. A consistent estimator of the variance of error component is also constructed. In addition, by using the smooth-threshold GMM estimating equations, we propose a variable selection method to identify the significant order of lagged terms automatically and remove the irrelevant regressors by setting their coefficient to zeros. As a result, it can consistently determine the true lagged order and specify the significant exogenous variables. Further studies show that the resulting estimator has the same asymptotic properties as if the true lagged order and significant regressors were known prior, i.e., achieving the oracle property. Numerical experiments are conducted to evaluate the finite sample performance of our procedures. An example of application is also illustrated.