FEASIBILITY OF THE REICH PROCEDURE IN THE DECOMPOSITION OF PLANE QUASICONFORMAL MAPPINGS

ＦＥＡＳＩＢＩＬＩＴＹＯＦＴＨＥＲＥＩＣＨＰＲＯＣＥＤＵＲＥＩＮＴＨＥＤＥＣＯＭＰＯＳＩＴＩＯＮＯＦＰＬＡＮＥＱＵＡＳＩＣＯＮＦＯＲＭＡＬＭＡＰＰＩＮＧＳ￥ＬＡＩＷＡＮＣＡＩ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＨｕａＱｉａ...     

没有Lipschitz假设的ψ-半压缩映象的不动点与ψ-强拟增生算子方程解的逼近

设X为实一致光滑Banach空间,T:D(T)∈X→X为ψ-半压缩映象且在它的不动点q处是局部有界的.本文证明了Mann迭代与Ishikawa迭代过程强收敛于T的唯一不动点g.几个相关的结果处理ψ-强拟增生算子方程的解的迭代构造.本文所得到的结果扩展并推广了Xu和Roach,Zhou和Jia等人的相应结果.     

Reich一个定理的改进及其应用

本文使用新的分析技巧研究了一致光滑Banach空间中一类增生映像的零点的迭代构造问题, 所得结果改进了Reich早期的一个著名定理.作为应用,导出了连续伪压缩映像的不动点的迭代算法的强收敛定理.     

On equivalence of generalized multi-valued contractions and Nadler's fixed point theorem

We consider two generalizations of Nadler's theorem, one proved by Mizoguchi and Takahashi in response to the Reich conjecture and another theorem proved by Kaneko. We show that due to the additional conditions of these theorems the given multi-valued map reduces to a multi-valued contraction map. We prove this result by showing that the orbit of the multi-valued map is bounded under the contractive conditions of the two generalizations.     

Fixed Points of Multivalued Contractions

A fixed-point theorem is proved for a broad class of closed-valued -contractions with for any positive t and with .     

一致光滑Banach空间中Φ-半压缩映象的不动点的迭代逼近

1　引言与预备知识设X为实Banach空间,X*为其共轭空间.正规对偶映象J:X→2X*定义为:Jx={x*∈X*:〈x,x*〉=‖x‖2=‖x*‖2},其中〈·,·〉表示广义对偶组.熟知,若X*为严格凸的,则J为单值正齐次的;若X*为一致凸的(等价地,X为一致光滑的),则J在X的任何有界子集上是一致连续的.我们用j表示单值的正规对偶映象.用R+表示正半实轴.以F(T)表示T的不动点集,即F(T)={x∈D(T):Tx=x}.映象T:D(T)X→X称为φ-半压缩的,如果F(T)≠,且存在严格增加函数φ:R+→R+,φ(0)=0,使得x∈D(T),y∈F(T),相应地存在某j(x-y)∈J(x-y)满足不等式〈Tx-y,j(…     

一致平滑Banach空间中一类非线性算子的Ishikawa迭代序列的收敛定理

使用新的技巧，我们得到了连续强增生算子或连续强伪压缩算子的Ｉｓｈｉｋａｗａ迭代序列的强收敛定理，推广或改进了近期相关的结果．