Altman型不动点定理的一些注记

Some Notes on Fixed Point Theorems of Altman-Type

针对Altman型不动点定理,讨论了在第一个指数参数分别大于1和在0和1之间,而第二个指数参数不小于0指数情形范数不等式条件下全连续算子不动点的存在性.证明了几个新的不动点定理.这些不等式条件与文献中已有条件不同,推广和补充了这些文献中的结果.结论对于更一般的半闭1-集压缩、凸幂凝聚和半闭凸幂1-集压缩算子也是成立的.

Fixed point theorems of Altman-type were studied. The existence of the fixed point of completely continuous operator was discussed under the norm inequality conditions that the first exponent parameter was respectively greater than 1 and between 0 and 1, at the same time, the second one was not less than 0. Some new fixed point theorems were proved. These inequality conditions were different from those as shown in earlier works in which the results were extended and supplemented. The conclusions were valid for more general operators such as semi-closed 1- set-contraction, convex-power condensing operator and semi-closed convex-power 1-set- contraction in references.