某类双调和映射的Landau型定理

令f(z)=h(z)+g(z)为开单位圆盘U内的调和映射.本文首先建立了有界调和映射的精确系数估计,其次得到了满足有界性条件|h(z)|+|g(z)|≤M的正规化调和映射的精确系数估计.作为其应用,得到了双调和映射的一些Landau型定理.这些结果改进和推广了早期作者的相关结果.     

多复变全纯映射正规族关于连续移动超平面的一个充要条件

证明了从C~n的一个区域到P~N(C)中的多复变全纯映射族为正规族的一个充要条件.这个充要条件与P~N(C)中的逐点处于一般位置的连续移动超平面族有关.证明的主要方法来自于微分方程.     

Banach空间中渐近非扩张非自身映射带误差Noor迭代的收敛性定理

本文主要对三个渐近非扩张非自身映射引入了一种新的投影型Noor迭代程序,并在一致凸Banach空间中给出了该Noor迭代序列的弱与强收敛性定理.我们的主要结果推广和改进了该领域许多近期的结果.     

How to recognize nonexpansive mappings and isometric mappings

In two real Banach spaces, we shall present two conditions, under one of which each nonexpansive mapping must be an isometry.     

Stability of multi-additive mappings in non-Archimedean normed spaces

A function f:Vn→W, where V is a commutative semigroup, W is a linear space and n?1 is an integer, is called multi-additive if it is additive in each variable. In this paper we prove the generalized Hyers-Ulam stability of multi-additive mappings in non-Archimedean normed spaces, using the so-called direct method.     

Numerical conformal mapping of multiply connected regions onto the second, third and fourth categories of Koebe?s canonical slit domains

This paper presents a boundary integral method for approximating the conformal mappings from any bounded or unbounded multiply connected region G onto the second, third and fourth categories of Koebe?s canonical slit domains. The method can be also used for calculating the conformal mappings of simply and doubly connected regions. The method is an extension of the author?s method for the first category of Koebe?s canonical slit domains (see [M.M.S. Nasser, Numerical conformal mapping via a boundary integral equation with the generalized Neumann kernel, SIAM J. Sci. Comput. 31 (2009) 1695-1715]). Three numerical examples are presented to illustrate the performance of the proposed method.     

Three-term conjugate gradient method for the convex optimization problem over the fixed point set of a nonexpansive mapping

Many constrained sets in problems such as signal processing and optimal control can be represented as a fixed point set of a certain nonexpansive mapping, and a number of iterative algorithms have been presented for solving a convex optimization problem over a fixed point set. This paper presents a novel gradient method with a three-term conjugate gradient direction that is used to accelerate conjugate gradient methods for solving unconstrained optimization problems. It is guaranteed that the algorithm strongly converges to the solution to the problem under the standard assumptions. Numerical comparisons with the existing gradient methods demonstrate the effectiveness and fast convergence of this algorithm.     

有限个平衡问题与非扩张映象不动点问题的复合迭代方法

在Hilbert空间中引进并研究一种新的复合粘性迭代算法,借以寻求有限个平衡问题的公共解集与非扩张映象不动点集的一个公共元素.所得结果改进并推广了最近一些人的最新结果.     

More on the averaged midpoint-trapezoid type rules

A generalization of the corrected averaged midpoint-trapezoid rule is derived. Various error bounds for this generalization are established.     

Convergence theorems for mixed equilibrium problems, variational inequality problem and uniformly quasi-?-asymptotically nonexpansive mappings

We introduce a modified block hybrid projection algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-?-asymptotically nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, the set of solutions of the mixed equilibrium problems. Then, we obtain strong convergence theorems for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works.