FIXED POINTS FOR WEAKLY INWARD MAPPINGS IN BANACH SPACES (Ⅱ)  

作　　者：Shaoyuan Xu Wangbin Xu Guanghui Zhou 

机构地区：[1]Hubei Normal University, China/Gannan Normal University, China [2]Hubei Normal University, China [3]Huaibei Normal University, China

出　　处：《Analysis in Theory and Applications》2010年第4期308-319,共12页分析理论与应用（英文刊）

基　　金：Supported in part by the Foundations of Education Ministry, Anhui Province, China (No: KJ2008A028);Education Ministry, Hubei Province, China (No: D20102502)

摘　　要：S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i（A, Ω, p） is equal to nonzero, where i（A, Ω, p） is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2].S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i（A, Ω, p） is equal to nonzero, where i（A, Ω, p） is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2].

关 键 词：fixed point and fixed point index weakly inward mapping completely contin-uous operator real Banach space cone 

分 类 号：O177.2[理学—数学] O189.11[理学—基础数学]