ITERATIVE APPROXIMATION OF FIXED POINTS FOR MULTIVALUED OPERATORS OF THE MONOTONE TYPE IN UNIFORMLY SMOOTH BANACH SPACES

In this paper, let K be a nonempty subset of a uniformly smooth Banach space X, and T:K→2~k be a multivalued operator of the monotone type. The iterative sequence which converges strongly to the unique fixed point of T is given. Our results are the extension and improvements of the results obtained previously by several authors including Dunn, Chidume, Deng and Ding.     

p一致凸Banach空间中渐近半压缩映象迭代过程的强收敛性

研究p一致凸Banach空间中渐近半压缩映象的修正的Mann迭代过程和修正的Ishikawa迭代过程的强收敛性.本文始终假设X是p一致凸Banach空间.最近,r-渐近半压缩映象的概念被引入,并给出了X中该映象(此时,r=p)的修正的Mann迭代过程和修正的Ishikawa迭代过程的强收敛性定理,文章所得结果改进、推广和统一了近期相关结果.     

广义集值强非线性混合似变分不等式解的迭代逼近

辅助原理的技巧被延拓来研究一类取非紧值的集值映象的广义强非线性混合似变分不等式.首先,证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性.其次,利用该存在性结果,给出了解这类广义强非线性混合似变分不等式的迭代算法.最后,不仅证明了这类广义强非线性混合似变分不等式解的存在性,而且证明了由算法生成的迭代序列的收敛性.     

关于增生算子方程解的Ishikawa迭代逼近

设X是任意实Banach空间,T:X→X是Lipschitz连续的增生算子.本文证明了,带误差的Ishikawa迭代序列强收敛到方程x Tx=f的唯一解.而且,还给Ishikawa迭代序列提供了一般的收敛率估计.利用该结果,本文推得,若T:X→X是Lipschitz连续的强增生算子,则带误差的Ishikawa迭代序列强收敛到方程Tx=f的唯一解.     

关于Banach空间中渐近非扩张型半群的不动点与渐近行为

Let X be a Banach space with a weakly continuous duality map Jφ,C a non-empty weakly compact convex subset of X, and T:(T(t):t∈S} an asymptotically nonexpansive type semigroup on C. In this paper, the inequality K∩F(T)≠0 is characterized, where K is a subset of C and F(T) is the set of all common fixed points of T. Furthermore, it is shown that an almost-orbit {u(t):t∈S} of T converges weakly to a point in F(T) if and only if {u(t):t∈S}is weakly asymptotically regular.     

关于增生算子方程的Ishikawa迭代法的收敛率估计

1 引言与预备知识设X是一实Banach空间,其对偶空间为X~*,记X与X~*之间的对偶对为(·,·),且     

用于解算子方程的Newton法的松弛收敛性

本文研究在适当条件下用于求算子方程F(x)=0的解的Newton法的收敛性。一方面,给出了解所在的区域和在该区域中解的唯一性,以及逼近解的新的收敛率估计。另一方面,也举例说明了理论结果应用于解Hammerstein型的非线性积分方程时,可给出解的存在唯一性与逼近解的收敛判据方面的结果。     

ISHIKAWA TYPE ITERATIVE SEQUENCES WITH ERRORS FOR LIPSCHITZIAN φ-STRONGLY ACCRETIVE OPERATOR EQUATIONS IN ARBITRARY BANACH SPACES

In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian (?)-strongly accretive operators and fixed points of Lipschitzian (?)-hemicontractive operators by Ishikawa type iterative sequences with errors. Our results unify , improve and extend the results obtained previously by several authors including Li and Liu (Acta Math. Sinica 41 (4)(1998), 845-850), and Osilike (Nonlinear Anal. TMA, 36(1)(1999), 1-9), and also answer completely the. open problems mentioned by Chidume (J. Math. Anal. Appl. 151(2) (1990), 453-461).     

ISHIKAWA TYPE ITERATIVE SEQUENCES WITH ERRORS FOR LIPSCHITZIAN ψ-STRONGLY ACCRETIVE OPERATOR EQUATIONS IN ARBITRARY BANACH SPACES

In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian ψ-strongly accretive operators and fixed points of Lipschitzian ψ-hemicontractive operators by lshikawa type iterative sequences with errors. Our results unify, improve and extend the results obtained previously by several authors including Li and Liu (Acta Math. Sinica 41 (4)(1998), 845-850), and Osilike (Nonlinear Anal. TMA, 36(1)(1999), 1-9), and also answer completely the open problems mentioned by Chidume (J. Math. Anal. Appl. 151 (2)(1990), 453-461).