Altman、Krasnoselskii和Petryshyn定理的推广

Some Generalizations of Altman's Theorem,Krasnoselskii's Theorem and Petryshyn's Theorem

利用不动点指数方法,本文借助于凸函数在内积空间中研究一类半闭1-集压缩算子方程解的存在性,获得了一些新的结果,推广Altman、Krasnoselskii和Petryshyn定理,并改进了相关文献中的结果.最后,我们给出主要结果的一个应用.

In this paper,utilizing the fixed point index method and using convex function,the existence of solutions for a class of semi-closed 1-set contractive operator equations in inner product spaces are discussed,and some new results are obtained,which generalized Altman＇s theorem,Krasnoselskii＇s theorem and Petryshyn＇s theorem,and improve some important results in the corresponding literatures.Finally,an example is given to illustrate our main results.