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中文摘要：
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.
英文摘要：
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.
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