摘要
本文证明Banach空间中无界域上一类弱序列连续和1-集弱压缩算子的若干新不动点定理.我们引入原点处弱半闭算子,得到该算子的若干不动点定理.进而将著名的Leray-Schauder不动点定理、Altman定理、Roth定理和Petryshyn定理推广到弱序列连续算子和1-集弱压缩算子以及原点处弱半闭算子的情形.本文的主要结果依赖于非紧性弱原子测度的有关条件.
The main purpose of this paper is to prove a collection of new fixed point theorems for weakly sequentially continuous and so-called 1-set weakly contractive operators on unbounded domains in Banach spaces.We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators.As consequences,we get the famous fixed point theorems of Leray-Schauder,Altman,Petryshyn and Rothe type in the case of weakly sequentially continuous,1-set weakly contractive （μ-nonexpansive） and weakly semi-closed operators at the origin and their generalizations.The main condition in our results is formulated in terms of axiomatic measures of weak nocompactness.
出处
《应用数学》
CSCD
北大核心
2013年第2期268-276,共9页
Mathematica Applicata
基金
Supported by the National Natural Science Foundation of China (10961003)
关键词
非紧性测度
弱凝聚和弱非扩张
弱序列连续
在原点弱半闭
不动点定理
Measures of weak noncompaetness
Weakly condensing and weakly nonexpansive
Weakly sequentially continuous
Weakly semi-closed at the origin
Fixedpoint theorem
