共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
The purpose of this article is two-fold. In the first place, we prove that a set is the image of a non empty closed convex subset of a real Banach space under an onto Fredholm operator of positive index if and only if it can be written as the union of {Dn:n∈N}, a non-decreasing family of non empty, closed, convex and bounded sets such that Dn+Dn+2⊆2Dn+1 for every n∈N. 相似文献
3.
Let H:Cn→Cn be a polynomial map, JH the Jacobian matrix of H , and VH the linear subspace of Mn(C) spanned by {JH(α)|α∈Cn}, the set of evaluated Jacobian matrices of H . We describe the dimension of VH through a power-linear Gorni–Zampieri mate of H, and give a numerical algorithm for computing this dimension and determining whether JH is additive-nilpotent, i.e., whether VH is a nilpotent subspace. 相似文献
4.
In this paper we give necessary and sufficient conditions for the system of positive numbers Mk1,Mk2,…,Mkd, 0≤k1<…<kd≤r, to guarantee the existence of an r -monotone function defined on the negative half-line R− and such that ‖x(ki)‖∞=Mki, i=1,2,…,d. We also discuss some applications of the obtained results and connections with other problems. 相似文献
5.
Let K be a compact convex subset of a real Hilbert space H; T:K→K a hemicontractive map. Let {αn} be a real sequence in [0,1] satisfying appropriate conditions; then for arbitrary x0∈K, the sequence {xn} defined iteratively by xn=αnxn−1+(1−αn)Txn, n≥1 converges strongly to a fixed point of T. 相似文献
6.
7.
8.
Let C be a closed convex subset of a real Hilbert space H and assume that T is an asymptotically κ-strict pseudo-contraction on C with a fixed point, for some 0≤κ<1. Given an initial guess x0∈C and given also a real sequence {αn} in (0, 1), the modified Mann’s algorithm generates a sequence {xn} via the formula: xn+1=αnxn+(1−αn)Tnxn, n≥0. It is proved that if the control sequence {αn} is chosen so that κ+δ<αn<1−δ for some δ∈(0,1), then {xn} converges weakly to a fixed point of T. We also modify this iteration method by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strongly convergent sequence. 相似文献
9.
10.
The approximation problem considered in the paper is to approximate a continuous multivariate function f(x)=f(x1,…,xd) by sums of two ridge functions in the uniform norm. We give a necessary and sufficient condition for a sum of two ridge functions to be a best approximation to f(x). This main result is next used in a special case to obtain an explicit formula for the approximation error and to construct one best approximation. The problem of well approximation by such sums is also considered. 相似文献
11.
Let R=(-∞,∞) and let Q∈C2:R→R+=[0,∞) be an even function. Then in this paper we consider the infinite–finite range inequality, an estimate for the Christoffel function, and the Markov–Bernstein inequality with the exponential weights wρ(x)=|x|ρe-Q(x),x∈R. 相似文献
12.
13.
Let X be a uniformly smooth Banach space, C be a closed convex subset of X, and A an m-accretive operator with a zero. Consider the iterative method that generates the sequence {xn} by the algorithm
where αn and γn are two sequences satisfying certain conditions, Jr denotes the resolvent (I+rA)−1 for r>0, and f:C→C be a fixed contractive mapping. Then as n→∞, the sequence {xn} strongly converges to a point in F(A). The results presented extends and improves the corresponding results of Hong-Kun Xu [Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631–643]. 相似文献
xn+1=αnf(xn)+(1−αn)Jrnxn,
14.
15.
In this paper we continue the study initiated in [15] concerning the obstacle problem for a class of parabolic non-divergence operators structured on a set of vector fields X={X1,…,Xq} in Rn with C∞-coefficients satisfying Hörmander?s finite rank condition, i.e., the rank of Lie[X1,…,Xq] equals n at every point in Rn. In [15] we proved, under appropriate assumptions on the operator and the obstacle, the existence and uniqueness of strong solutions to a general obstacle problem. The main result of this paper is that we establish further regularity, in the interior as well as at the initial state, of strong solutions. Compared to [15] we in this paper assume, in addition, that there exists a homogeneous Lie group G=(Rn,°,δλ) such that X1,…,Xq are left translation invariant on G and such that X1,…,Xq are δλ-homogeneous of degree one. 相似文献
16.
17.
Let K be a nonempty closed convex subset of a Banach space E, T:K→K a continuous pseudo-contractive mapping. Suppose that {αn} is a real sequence in [0,1] satisfying appropriate conditions; then for arbitrary x0∈K, the Mann type implicit iteration process {xn} given by xn=αnxn−1+(1−αn)Txn,n≥0, strongly and weakly converges to a fixed point of T, respectively. 相似文献
18.
19.
Kai-Uwe Schmidt 《Comptes Rendus Mathematique》2014,352(2):95-97
We give a solution to an extremal problem for polynomials, which asks for complex numbers α0,…,αn of unit magnitude that minimise the largest supremum norm on the unit circle for all polynomials of degree n whose k -th coefficient is either αk or −αk. 相似文献