Effective results on a fixed point algorithm for families of nonlinear mappings

We use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by López-Acedo and Xu to find common fixed points of finite families of k-strict pseudocontractive self-mappings of convex subsets of Hilbert spaces. We show that these results are guaranteed by a number of logical metatheorems for classical and semi-intuitionistic systems.     

Strong convergence of an iterative algorithm for an infinite family of strict pseudo-contractions in Banach spaces

In this paper, we introduce a new W-mapping and present an iterative algorithm for an infinite family of strict pseudo-contractions. Strong convergence theorems are proved in Banach spaces. Our results improve and extend the corresponding result announced by Cai and Hu [G. Cai, C. Hu, Strong convergence theorems of modified Ishikawa iterative process with errors for an infinite family of strict pseudo-contractions, Nonlinear Anal. 71(12) (2009) 6044-6053].     

Convergence of ‖π approximations to the strict approximation in R n

Suppose V is a subspace of R ⁿ and assume that ‖_∞-norm is obtained as a suitable limit of convex functions {π _m }. Let x _m be a best π _m -approximation to x by elements of V. We prove that the sequence x _m converges to the strict best approximation of x. As a crollary we obtain convergence of the best ‖_πm -approximation.     

Asymptotic expression of the linear discrete best -approximation

Let h_p, 1<p<∞, be the best ℓ_p-approximation of the element from a proper affine subspace K of , hK, and let denote the strict uniform approximation of h from K. We prove that there are a vector and a real number a, 0a1, such that

for all p>1, where with γ_p=o(a^p/p).     

Analytic hypoellipticity in the presence of nonsymplectic characteristic points

Recently, N. Hanges proved that the operator

     

Banach空间中非线性混合型脉冲积微分方程的解

本文讨论Ｂａｎａｃｈ空间中带定时脉冲的非线性混合型积微分方程，利用Ｄａｒｂｏ不动点定理与增算子不动点定理证明了解与最大解和最小解的存在性，得到了最大解和最小解的迭代公式．     

4一致(ξ)-超图的最小边数的上界

主要讨论了4一致l-超图的最小边数与最小上色数的关系,给出了上色数为3的4一致l-超图的最小边数的一个上界.     

Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces

The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.