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Fixed points for weakly inward mappings in Banach spaces |
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| Authors: | Shaoyuan Xu Baoguo Jia |
| Institution: | a Department of Mathematics, Nanjing University, Nanjing 210093, PR China b Department of Mathematics and Computer Science, Gannan Teachers College, Ganzhou 341000, PR China c Mathematics and Scientific Computer College, Zhongshan University, Guangzhou 510275, PR China d Department of Mathematics, Jiangxi Normal University, Nanchang 330027, PR China |
| Abstract: | S. Hu and Y. Sun S. Hu, Y. Sun, Fixed point index for weakly inward mappings, J. Math. Anal. Appl. 172 (1993) 266-273] defined the fixed point index for weakly inward mappings, investigated its properties and studied the fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we continue to investigate boundary conditions, under which the fixed point index for the completely continuous and weakly inward mapping, denoted by i(A,Ω,P), is equal to 1 or 0. Correspondingly, we can obtain some new fixed point theorems of the completely continuous and weakly inward mappings and existence theorems of solutions for the equations Ax=μx, which extend many famous theorems such as Leray-Schauder's theorem, Rothe's two theorems, Krasnoselskii's theorem, Altman's theorem, Petryshyn's theorem, etc., to the case of weakly inward mappings. In addition, our conclusions and methods are different from the ones in many recent works. |
| Keywords: | Fixed point and fixed point index Weakly inward mapping Completely continuous operator Real Banach space Cone |
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