Applied Mathematics-A Journal of Chinese Universities

In this paper, the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are investigated. Some necessary condition and sufficient condition for the convergence of iterative sequences are given respectively. The results thus extend and improve some recent corresponding results.

An existence and uniqueness results concerned with the Dirichlet boundary value problem u"+cu'+g(t,u)=e(t),u(0)=u(π)=0 is offered.

In this paper, lower bounds of the topological entropy for nonautonomous dynamical systems are given via the growths of topological complexity in fundamental group and in degree.

A locally semicomplete digraph is a digraph D = (V,A) satisfying the following condition: for every vertex x ∈ V the D[O(x)] and D[I(x)] are semicomplete digraphs. In this paper, we get some properties of cycles and determine the exponent set of primitive locally semicomplete digraphs.

The MTD (mixture transition distribution) model based on Weibull distribution (WMTD model) is proposed in this paper, which is aimed at its parameter estimation. An EM algorithm for estimation is given and shown to work well by some simulations. And bootstrap method is used to obtain confidence regions for the parameters. Finally, the results of a real example—predicting stock prices—show that the WMTD model proposed is able to capture the features of the data from thick-tailed distribution better than GMTD (mixture transition distribution) model.

Let (X1,X2,…,Xn) and (Y1,Y2,…,Yn) be real random vectors with the same marginal distributions, if (X1,X2,…,Xn)≤ c (Y1,Y2,…,Yn, it is showed in this paper that Σ =1 X i≤ cx Σ Yi and max1≤k≤n Σ X i≤ icx max 1≤k≤n Σ Yi hold. Based on this fact, a more general comparison theorem is obtained.

Let 0<λ1,λ2<1 and 1λ1-λ2≥ max {λ1,λ2}. Let (λ1,λ2) be the attractor of the iterated function system {φ1,φ2} on the line, where φ1(itx)=λ1 x and φ2(x)=1−λ1+λ1 x,x∈R. K(λ1,λ2) is called a non-symmetry Cantor set. In this paper, it is proved that the exact Hausdorff centred measure of K(λ1,λ2) equals 2 s (1−λ) s , where λ=max{λ1,λ2} and s is the Hausdorff dimension of K(λ1,λ2).

In this paper, by using the theory of semigroup and spectrum, a computation formula on the growth order of one class ofC 0-semigroups in Banach space is proved.

The monotonicity of a rational Bézier curve, usually related to an explicit function, is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the affine invariant property, a kind of generalized monotonicity, called direction monotonicity, is introduced for rational Bézier curves. The direction monotonicity is applied to both planar and space curves and to both Cartesian and affine coordinate systems, and it includes the traditional monotonicity as a subcase. By means of it, proper affine coordinate systems may be chosen to make some rational Bézier curves monotonic. Direction monotonic interpolation may be realized for some of the traditionally nonmonotonic data as well.